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Existence and approximation of solutions for a class of degenerate elliptic equations with Neumann boundary condition


Abstract


In this work we study the equation Lu=f, where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set {\Omega}. We prove the existence and uniqueness of weak solutions in the weighted Sobolev space {\mathrm{W}}^{1,2}(\Omega , \omega) for the Neumann problem. The main result establishes that a weak solution of degenerate elliptic equations can be approximated by a sequence of solutions for non-degenerate elliptic equations

DOI Code: 10.1285/i15900932v40n2p63

Keywords: Neumann problem; weighted Sobolev spaces

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