Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$
Alberto Fıorenza, Carlo Sbordone · Studia Mathematica · 1998
We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here $f ∈ L^1(Ω)$ and the solution belongs to the so-called grand Sobolev space $W_0^{1,2)}(Ω)$. This is the proper spac