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arXiv · 1310.5907

Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces

J. V. Goncalves·M. L. M. Carvalho
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Abstract

We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation $\displaystyle -\mbox{div} (ϕ(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in} Ω$ under Dirichlet boundary conditions, where $Ω\subset {\bf R}^{N}$ is a bounded smooth domain, $ϕ: (0,\infty)\longrightarrow (0,\infty)$ is a suitable continuous function and $f: Ω\times {\bf R} \to {\bf R}$ satisfies the Carathéodory conditions, while $h$ is a measure.

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J. V. Goncalves, M. L. M. Carvalho. 2013-10-22. Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces. https://arxiv.org/abs/1310.5907

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