The Boundary Harnack Inequality for Solutions to Equations of Aronsson type in the Plane
2011 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 36, 261-278 p.Article in journal (Refereed) Published
In this paper we prove a boundary Harnack inequality for positive functions which vanish continuously on a portion of the boundary of a bounded domain \Omega \subset R2 and which are solutions to a general equation of p-Laplace type, 1 < p < \infty. We also establish the same type of result for solutions to the Aronsson type equation \nabla (F(x,\nabla u)) \cdot F\eta(x,\nabla u) = 0. Concerning \Omega we only assume that \partial\Omega is a quasicircle. In particular, our results generalize the boundary Harnack inequalities in [BL] and [LN2] to operators with variable coefficients.
Place, publisher, year, edition, pages
Academia Scientiarum Fennica , 2011. Vol. 36, 261-278 p.
Boundary Harnack inequality, p-Laplace, A-harmonic function, infinity harmonic function, Aronsson type equation, quasicircle
IdentifiersURN: urn:nbn:se:umu:diva-40225DOI: 10.5186/aasfm.2011.3616OAI: oai:DiVA.org:umu-40225DiVA: diva2:398453