L²-data Dirichlet problem for weighted form Laplacians
We solve the L²-data Dirichlet boundary problem for a weighted form Laplacian in the unit Euclidean ball. The solution is given explicitly as a sum of four series.
Laplace type operators: Dirichlet problem
We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into -irreducible subspaces.
Large solutions for the laplacian with a power nonlinearity given by a variable exponent
Le rôle de la frontière dans un problème elliptique avec non-linéarité critique et conditions au bord de Neumann
Lp regularity of the Dirichlet problem for elliptic equations with singular drift.