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Equações diferenciais parciais elípticas multivalentes: crescimento crítico, métodos variacionais

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Bibliographic Details
Main Author: Carvalho, Marcos Leandro Mendes
Publication Date: 2013
Format: Doctoral thesis
Language: por
Source: Repositório Institucional da UFG
Download full: http://repositorio.bc.ufg.br/tede/handle/tede/3686
Summary: In this work we develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity, minimization and compactness techniques to investigate existence of solution of the multivalued equation −∆Φu ∈ ∂ j(.,u) +λh in Ω, where Ω ⊂ RN is a bounded domain with boundary smooth ∂Ω, Φ : R → [0,∞) is a suitable N-function, ∆Φ is the corresponding Φ−Laplacian, λ > 0 is a parameter, h : Ω → R is a measurable and ∂ j(.,u) is a Clarke’s Generalized Gradient of a function u %→ j(x,u), a.e. x ∈ Ω, associated with critical growth. Regularity of the solutions is investigated, as well.
Summary:In this work we develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity, minimization and compactness techniques to investigate existence of solution of the multivalued equation −∆Φu ∈ ∂ j(.,u) +λh in Ω, where Ω ⊂ RN is a bounded domain with boundary smooth ∂Ω, Φ : R → [0,∞) is a suitable N-function, ∆Φ is the corresponding Φ−Laplacian, λ > 0 is a parameter, h : Ω → R is a measurable and ∂ j(.,u) is a Clarke’s Generalized Gradient of a function u %→ j(x,u), a.e. x ∈ Ω, associated with critical growth. Regularity of the solutions is investigated, as well.

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