Abstract

CASTRO T., RAFAEL A.. Regularity of the solutions for a Robin problem and some applications. Rev.colomb.mat. [online]. 2008, vol.42, n.2, pp.127-144. ISSN 0034-7426.

In this paper we study the regularity of the solutions for a Robin problem, with a nonlinear term with sub-critical growth respect to a variable. We establish the Sobolev space H¹(Ω) as the orthogonal sum of two subspaces, and we give the first step to demonstrate the existence of solutions of our problem.

Keywords : Robin problems; trace operators; variational formulation; weaksolutions; Sobolev spaces; bootstrapping; Green formula; orthogonal sum of subspace.

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