On a class of intermediate local-nonlocal elliptic problems - Alves, Claudianor O.; Corrêa, Francisco Julio S. A.; Chipot, Michel (Topological Methods in Nonlinear Analysis, 2016)
This paper is concerned with the existence of solutions for a class of intermediate local-nonlocal boundary value problems of the following type: -div [a(_Ω (x,r)u(y)dy) abla u] = f(x,u, abla u ) in Ω, uH_0^1(Ω ), (IP) % where Ω is a bounded domain of R^N, aR → R is a continuous function, fΩ × R × R^N is a given function, r> 0 is a fixed number, Ω (x,r)=Ω B(x,r), where B(x,r)={ yR^N: |y-x|< r}. Here |· | is the Euclidian norm, _Ω (x,r)u(y)dy=1meas.06em(Ω (x,r))_Ω (x,r)u(y)dy and meas.06em(X) denotes the Lebesgue measure of a measurable set XR^N.