Entropy solution to an elliptic problem with nonlinear boundary conditions
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.
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.
Full Text:
PDFDOI: https://doi.org/10.52846/ami.v39i2.433