Entropy solution to an elliptic problem with nonlinear boundary conditions

Stanislas Ouaro, Arouna Ouedraogo

Abstract


In this paper, we consider the equation $b(u) - div~a(u,Du) = f$ in a bounded domain with nonlinear boundary conditions
of the form $-a(u,Du).\eta \in \beta(x,u)$. We introduce a notion of entropy solution for this problem and prove existence and uniqueness
of this solution for general $L^{1}-$data.

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