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arXiv · 2207.07323

Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces

Giuseppina Barletta·Andrea Cianchi·Greta Marino
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Abstract

Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established under boundary conditions of Dirichlet, or Neumann, or Robin type. A decisive role in the results is played by optimal forms of Orlicz-Sobolev embeddings and boundary trace embeddings, which allow for critical growths of the coefficients.

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Giuseppina Barletta, Andrea Cianchi, Greta Marino. 2022-07-15. Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces. https://arxiv.org/abs/2207.07323

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