Entropy solution to nonlinear multivalued elliptic problem with variable exponents and measure data

Ismael Nyanquini, Stanislas Ouaro, Safimba Soma

Abstract


We study a nonlinear elliptic problem governed by a general
Leray-Lions operator with variable exponents and diffuse Radon
measure data that does not charge the sets of zero $p(.)$-capacity. We prove a decomposition theorem for these
measures (more precisely, as a sum of a function in
$L^{1}(\Omega)$ and of a measure in $W^{-1,p'(.)}(\Omega)$) and an existence and uniqueness result of entropy solution.


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