Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. By using a lin...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Hindawi Limited
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/1e8d288e5550485b8913742e5f0d0855 |
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| Sumario: | In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. By using a linear functional analysis method, we provide sufficient conditions which ensure that the solution set of the equation is nonempty, and it possesses a greatest element and a smallest element with respect to the ordering “≤,” which are called barrier solutions. |
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