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

被引：6

作者：

Barletta, Giuseppina ^{[1
]}

Cianchi, Andrea ^{[2
]}

Marino, Greta ^{[3
]}

机构：

[1] Univ Mediterranea Reggio Calabria, Dipartimento Ingn Civile Energia Ambiente & Mat, Via Zehender, I-89122 Reggio Di Calabria, Italy

[2] Univ Firenze, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[3] Univ Augsburg, Inst Math, Univ Str 2, D-86159 Augsburg, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 02期

关键词：

35J25; 35J60; 35B65; DIFFERENTIAL-EQUATIONS; SOBOLEV EMBEDDINGS; EIGENVALUE PROBLEM; REGULARITY; GROWTH; SUPERSOLUTIONS; THEOREM;

D O I：

10.1007/s00526-022-02393-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：42

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