Hölder continuity of solutions to the A-Laplace equation involving measures

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September 2009, 8(5): 1577-1583. doi: 10.3934/cpaa.2009.8.1577

Hölder continuity of solutions to the $A$-Laplace equation involving measures

Samia Challal ^1, and Abdeslem Lyaghfouri ^1,

1.	Fields Institute, 222 College Street, Toronto M5T 3J1, Canada, Canada

Received April 2007 Revised March 2009 Published April 2009

Abstract
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We show an optimal Hölder continuity for the solutions of the equation $- \Delta_A u=\mu$ provided that $\mu (B(x,r)) \leq C r^{n-1} $ for any ball $B(x,r)\subset \Omega$, with $r\leq 1$.

Keywords: Radon measure, A-Laplacian, Hölder continuity..

Mathematics Subject Classification: Primary: 35J60, 35J70, 35B6.

Citation: Samia Challal, Abdeslem Lyaghfouri. Hölder continuity of solutions to the $A$-Laplace equation involving measures. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1577-1583. doi: 10.3934/cpaa.2009.8.1577

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