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A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2012 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 191, no 1, 1-23 p.Article in journal (Refereed) Published
Abstract [en]

We consider non-negative solutions to a class of second-order degenerate Kolmogorov operators of the form L=Sigma(m)(i,j=1)a(i,j)(z)partial derivative(xixj)+Sigma(m)(i=1)a(i)(z)partial derivative(xi)+Sigma(N)(i,j=1)b(i,j)x(i)partial derivative(xj)-partial derivative(t), where z = (x, t) belongs to an open set Omega subset of R-N x R, and 1 <= m <= N. Let (z) over bar is an element of Omega, let K be a compact subset of (Omega) over bar, and let Sigma subset of partial derivative Omega be such that K boolean AND partial derivative Omega subset of Sigma. give sufficient geometric conditions for the validity of the following Carleson type estimate. There exists a positive constant C-K, depending only on Omega, Sigma, K, (z) over tilde and on L, such that sup(K) u <= C(K)u((z) over tilde), for every non-negative solution u of Lu = 0 in Omega such that u|(Sigma) = 0.

Place, publisher, year, edition, pages
2012. Vol. 191, no 1, 1-23 p.
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URN: urn:nbn:se:umu:diva-53272DOI: 10.1007/s10231-010-0172-zISI: 000298648300001OAI: diva2:511716
Available from: 2012-03-23 Created: 2012-03-19 Last updated: 2014-04-07Bibliographically approved

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Nyström, Kaj
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