Existence and optimal regularity theory for weak solutions of free transmission problems of quasilinear type via Leray-Lions method

Diego R. Moreira, Harish Shrivastava

We study existence and regularity of weak solutions for the following PDE $$ -\dive(A(x,u)|\nabla u|^{p-2}\nabla u) = f(x,u),\;\;\mbox{in $B_1$}. $$ where $A(x,s) = A_+(x)χ_{\{s>0\…