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

Samia Challal; Abdeslem Lyaghfouri

doi:10.3934/cpaa.2009.8.1577

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2009, Volume 8, Issue 5: 1577-1583. Doi: 10.3934/cpaa.2009.8.1577

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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

Received: March 31, 2007

Revised: February 28, 2009

Published: August 2009

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Abstract

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 $r\leq 1$.

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Mathematics Subject Classification: Primary: 35J60, 35J70, 35B65.

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