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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

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