We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class Ap. The argument is a ...

We study the problem -Δu=f, where f has a point-singularity. In particular, we are interested in f = δx0, a Dirac delta with support in x0, but singularities of the form f|x - x0|-s are also considered. We prove the stability ...

Let be a polygonal domain in R2 and let U be a weak solution of u = f in with Dirichlet boundary condition, where f 2 Lp !( ) and ! is a weight in Ap(R2), 1 < p < 1. We give some estimates of the Green function ...

Let Ω be a nonempty open proper and connected subset of Rn, n≥3. Consider the elliptic Schrödinger type operator LEu=AEu+Vu=−Σijaij(x)uxixj+Vu in Ω, and the linear parabolic operator LPu=APu+Vu= ut−Σaij(x,t)uxixj+Vu in ...

Let u be a weak solution of the equation (-Δ)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ ℝn. In this paper, we obtain some estimates for the Green's function associated to this problem. Moreover, ...

Let Ω be a bounded domain in R n with C 2 and let u be a solution of the classical Poisson problem in ; i.e., { u = f in , u = 0 on , where f L p ( ) and is a weight in A p . The main goal of this paper is to prove the ...