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Publications (10 of 36) Show all publications
Lundström, N. L. P. & Singh, J. (2023). Estimates of p-harmonic functions in planar sectors. Arkiv för matematik, 61(1), 141-175
Open this publication in new window or tab >>Estimates of p-harmonic functions in planar sectors
2023 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 61, no 1, p. 141-175Article in journal (Refereed) Published
Abstract [en]

Suppose that p∈(1,∞], ν∈[1/2,∞), Sν= {(x1, x2)∈R2\{(0, 0)}:|φ|< π/2ν}, where φ is the polar angle of (x1, x2). Let R>0 and ωp(x) be the p-harmonic measure of ∂B(0,R)∩Sν at x with respect to B(0,R)∩Sν. We prove that there exists a constant C such that whenever x∈B(0,R)∩S2ν and where the exponent k(ν, p) is given explicitly as a function of ν and p. Using this estimate we derive local growth estimates for p-sub- and p-superharmonic functions in planar domains which are locally approximable by sectors, e.g., we conclude bounds of the rate of convergence near the boundary where the domain has an inwardly or outwardly pointed cusp. Using the estimates of p-harmonic measure we also derive a sharp Phragmén-Lindelöf theorem for p-subharmonic functions in the unbounded sector Sν. Moreover, if p=∞ then the above mentioned estimates extend from the setting of two-dimensional sectors to cones in Rn. Finally, when ν∈(1/2,∞) and p∈(1,∞) we prove uniqueness (modulo normalization) of positive p-harmonic functions in Sν vanishing on ∂Sν.

Place, publisher, year, edition, pages
International Press of Boston, 2023
Keywords
Growth estimate, Harmonic measure, Infinity harmonic measure, Infinity Laplace equation, Laplace equation, Laplacian, P harmonic measure, P Laplace equation, Phragmen Lindelöf principle
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-209121 (URN)10.4310/ARKIV.2023.v61.n1.a8 (DOI)001001371700008 ()2-s2.0-85159226633 (Scopus ID)
Funder
Swedish Research Council, 2018-03743
Available from: 2023-06-07 Created: 2023-06-07 Last updated: 2023-09-05Bibliographically approved
Lundström, N. & Söderbacka, G. (2022). Estimates of size of cycle in a predator-prey system. Differential Equations and Dynamical Systems, 30(1), 131-159
Open this publication in new window or tab >>Estimates of size of cycle in a predator-prey system
2022 (English)In: Differential Equations and Dynamical Systems, ISSN 0971-3514, E-ISSN 0974-6870, Vol. 30, no 1, p. 131-159Article in journal (Refereed) Published
Abstract [en]

We consider a Rosenzweig–MacArthur predator-prey system which incorporates logistic growth of the prey in the absence of predators and a Holling type II functional response for interaction between predators and preys. We assume that parameters take values in a range which guarantees that all solutions tend to a unique limit cycle and prove estimates for the maximal and minimal predator and prey population densities of this cycle. Our estimates are simple functions of the model parameters and hold for cases when the cycle exhibits small predator and prey abundances and large amplitudes. The proof consists of constructions of several Lyapunov-type functions and derivation of a large number of non-trivial estimates which are of independent interest.

Place, publisher, year, edition, pages
Springer, 2022
Keywords
Locating limit cycle, Locating attractor, Size of limit cycle, Lyapunov function, Lyapunov stability
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-153284 (URN)10.1007/s12591-018-0422-x (DOI)000759639300008 ()2-s2.0-85081348740 (Scopus ID)
Available from: 2018-11-15 Created: 2018-11-15 Last updated: 2022-07-12Bibliographically approved
Lundström, N. L. P. (2022). Growth of subsolutions to fully nonlinear equations in halfspaces. Journal of Differential Equations, 320, 143-173
Open this publication in new window or tab >>Growth of subsolutions to fully nonlinear equations in halfspaces
2022 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 320, p. 143-173Article in journal (Refereed) Published
Abstract [en]

We characterize lower growth estimates for subsolutions in halfspaces of fully nonlinear partial differential equations on the form F(x,u,Du,D2u)=0 in terms of solutions to ordinary differential equations built upon assumptions on F. Using this characterization we derive several sharp Phragmen–Lindelöf-type theorems for certain classes of well known PDEs. The equation need not be uniformly elliptic nor homogeneous and we obtain results both in case the subsolution is bounded or unbounded. Among our results we retrieve classical estimates in the halfspace for p-subharmonic functions and extend those to more general equations; we prove sharp growth estimates, in terms of k and the asymptotic behavior of 0RC(s)ds, for subsolutions of equations allowing for sublinear growth in the gradient of the form C(|x|)|Du|k with k≥1; we establish a Phragmen–Lindelöf theorem for weak subsolutions of the variable exponent p-Laplace equation in halfspaces, 1<p(x)<∞, p(x)∈C1, of which we conclude sharpness by finding the "slowest growing" p(x)-harmonic function together with its corresponding family of p(x)-exponents. The paper ends with a discussion of our results from the point of view of a spatially dependent diffusion problem.

Place, publisher, year, edition, pages
Academic Press, 2022
Keywords
Non homogeneous, Non standard growth, Phragmen Lindelöf, Quasi linear, Sub linear, Variable exponent
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-193056 (URN)10.1016/j.jde.2022.02.048 (DOI)000792903800005 ()2-s2.0-85125776862 (Scopus ID)
Funder
Swedish Research Council, 2018-03743
Available from: 2022-03-21 Created: 2022-03-21 Last updated: 2023-09-05Bibliographically approved
Olofsson, M., Önskog, T. & Lundström, N. L. P. (2022). Management strategies for run-of-river hydropower plants: an optimal switching approach. Optimization and Engineering, 23(3), 1707-1731
Open this publication in new window or tab >>Management strategies for run-of-river hydropower plants: an optimal switching approach
2022 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 23, no 3, p. 1707-1731Article in journal (Refereed) Published
Abstract [en]

The mathematical theory for optimal switching is by now relatively well developed, but the number of concrete applications of this theoretical framework remains few. In this paper, we bridge parts of this gap by applying optimal switching theory to a conceptual production planning problem related to hydropower. In particular, we study two examples of small run-of-river hydropower plants and provide an outline of how optimal switching can be used to create fully automatic production schemes for these. Along the way, we create a new model for random flow of water based on stochastic differential equations and fit this model to historical data. We benchmark the performance of our model using actual flow data from a small river in Sweden and find that our production scheme lies close to the optimal, within 2 and 5 %, respectively, in a long term investigation of the two plants considered.

Place, publisher, year, edition, pages
Springer, 2022
Keywords
Optimization, Partial differential equation, Production planning, River flow model, Stochastic differential equation, Variational inequality
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-187459 (URN)10.1007/s11081-021-09683-3 (DOI)000692437400001 ()2-s2.0-85114160527 (Scopus ID)
Funder
Swedish Research Council, 2018-03743
Available from: 2021-09-13 Created: 2021-09-13 Last updated: 2022-12-19Bibliographically approved
Román, S., Stahel, A., Gilthorpe, J. D., Eddebo, J. & Lundström, N. (2022). Serious side effects exceed the risk of hospitalization with COVID-19 in the Swedish population.
Open this publication in new window or tab >>Serious side effects exceed the risk of hospitalization with COVID-19 in the Swedish population
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2022 (English)Other (Refereed)
National Category
Public Health, Global Health, Social Medicine and Epidemiology
Identifiers
urn:nbn:se:umu:diva-203205 (URN)
Note

Published 2022-07-15

Available from: 2023-01-16 Created: 2023-01-16 Last updated: 2023-01-16Bibliographically approved
Lundström, N. L. P., Olofsson, M. & Toivanen, O. (2022). Strong maximum principle and boundary estimates for nonhomogeneous elliptic equations. Potential Analysis
Open this publication in new window or tab >>Strong maximum principle and boundary estimates for nonhomogeneous elliptic equations
2022 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear nonhomogeneous degenerate elliptic equations on the formF(x, u, Du, D2u) = 0 under suitable assumptions allowing for non-Lipschitz growth in the gradient term. In case of smooth boundaries, we also prove a Hopf lemma, a boundary Harnack inequality, and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary. Our results apply, e.g., to weak solutions of an eigenvalue problem for the variable exponent p-Laplacian.

Place, publisher, year, edition, pages
Springer, 2022
Keywords
Boundary Harnack inequality, Fully nonlinear, Hopf Lemma, Laplace equation, Non-Lipschitz drift, Non-standard growth, Osgood condition, Sphere condition, Variable exponent
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-202256 (URN)10.1007/s11118-022-10055-4 (DOI)000904962800001 ()2-s2.0-85144849432 (Scopus ID)
Funder
Swedish Research Council, 2018-03743
Available from: 2023-01-05 Created: 2023-01-05 Last updated: 2023-09-05
Littorin, N., Stahel, A., Engwall, A.-C., Hultborn, R., Blomberg, S., Weiss, L., . . . Wadenbäck, J. (2022). Swedish Public Health Agency reporting has distorted mortality rates for the unvaccinated and the vaccinated.
Open this publication in new window or tab >>Swedish Public Health Agency reporting has distorted mortality rates for the unvaccinated and the vaccinated
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2022 (English)Other (Other academic)
National Category
Public Health, Global Health, Social Medicine and Epidemiology
Identifiers
urn:nbn:se:umu:diva-203206 (URN)
Available from: 2023-01-16 Created: 2023-01-16 Last updated: 2023-09-27Bibliographically approved
Lundström, N. L. .. & Olofsson, M. (2022). Systems of Fully Nonlinear Parabolic Obstacle Problems with Neumann Boundary Conditions. Applied mathematics and optimization, 86(2), Article ID 27.
Open this publication in new window or tab >>Systems of Fully Nonlinear Parabolic Obstacle Problems with Neumann Boundary Conditions
2022 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 86, no 2, article id 27Article in journal (Refereed) Published
Abstract [en]

We prove the existence of a unique viscosity solution to certain systems of fully nonlinear parabolic partial differential equations with interconnected obstacles in the setting of Neumann boundary conditions. The method of proof builds on the classical viscosity solution technique adapted to the setting of interconnected obstacles and construction of explicit viscosity sub- and supersolutions as bounds for Perron’s method. Our motivation stems from so called optimal switching problems on bounded domains.

Place, publisher, year, edition, pages
Springer, 2022
Keywords
Optimal switching, Multi modes switching, Constraints, Fully nonlinear PDE, Neumann boundary condition, Viscosity solution, Barrier
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-199057 (URN)10.1007/s00245-022-09890-z (DOI)000825422400012 ()2-s2.0-85133688762 (Scopus ID)
Funder
Swedish Research Council, 2018-03743
Available from: 2022-09-01 Created: 2022-09-01 Last updated: 2022-09-06Bibliographically approved
Lundström, N. L. .., Olofsson, M. & Önskog, T. (2019). Existence, uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching. Journal of Mathematical Analysis and Applications, 475(1), 13-31
Open this publication in new window or tab >>Existence, uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching
2019 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 475, no 1, p. 13-31Article in journal (Refereed) Published
Abstract [en]

We study viscosity solutions to a system of nonlinear degenerate parabolic partial integrodifferential equations with interconnected obstacles. This type of problem occurs in the context of optimal switching problems when the dynamics of the underlying state variable is described by an n-dimensional L´evy process. We first establish a continuous dependence estimate for viscosity sub- and supersolutions to the system under mild regularity, growth and structural assumptions on the partial integro-differential operator and on the obstacles and terminal conditions. Using the continuous dependence estimate, we obtain the comparison principle and uniqueness of viscosity solutions as well as Lipschitz regularity in the spatial variables. Our main contribution is construction of suitable families of viscosity sub- and supersolutions which we use as “barrier functions” to prove Ho¨lder continuity in the time variable, and, through Perron’s method, existence of a unique viscosity solution. This paper generalizes parts of the results of Biswas, Jakobsen and Karlsen (2010) and of Lundström, Nyström and Olofsson (2014) to hold for more general systems of equations.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
variational inequality, existence, viscosity solution, nonlocal operator, partial integro-differential operator, Lévy process, jump diffusion, optimal switching problem, regularity, continuous dependence, well posed
National Category
Mathematics Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-153270 (URN)10.1016/j.jmaa.2018.11.003 (DOI)000464490800002 ()2-s2.0-85061800225 (Scopus ID)
Available from: 2018-11-14 Created: 2018-11-14 Last updated: 2023-03-24Bibliographically approved
Lundström, N. L. P., Loeuille, N., Meng, X., Bodin, M. & Brännström, Å. (2019). Meeting yield and conservation objectives by harvesting both juveniles and adults. American Naturalist, 193(3), 373-390
Open this publication in new window or tab >>Meeting yield and conservation objectives by harvesting both juveniles and adults
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2019 (English)In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 193, no 3, p. 373-390Article in journal (Refereed) Published
Abstract [en]

Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as "pretty good yields" (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured model and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, although our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g., basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and size structure, so that these later quantities can provide integrative signals to detect possible collapses.

Place, publisher, year, edition, pages
University of Chicago Press, 2019
Keywords
fisheries management, maximum sustainable yield, pretty good yield, Pareto front, resilience, size structure
National Category
Ecology Evolutionary Biology
Identifiers
urn:nbn:se:umu:diva-155571 (URN)10.1086/701631 (DOI)000459624900007 ()30794450 (PubMedID)2-s2.0-85060768325 (Scopus ID)
Available from: 2019-01-22 Created: 2019-01-22 Last updated: 2023-03-24Bibliographically approved
Projects
Viscosity solutions to systems of variational inequalities related to multi-modes switching problems [2018-03743_VR]; Umeå University
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4040-8142

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