Multiple solutions for some strongly degenerate second order elliptic equations

Autor:	João R. Santos Júnior, Gaetano Siciliano
Rok vydání:	2022
Předmět:	Physics Sobolev space Pure mathematics EQUAÇÕES DIFERENCIAIS PARCIAIS General Mathematics Operator (physics) Bounded function Degenerate energy levels Mathematics::Analysis of PDEs Order (ring theory) Nabla symbol Boundary value problem Domain (mathematical analysis)
Zdroj:	Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP
ISSN:	1875-8576 0921-7134
DOI:	10.3233/asy-211728
Popis:	We consider a boundary value problem in a bounded domain involving a degenerate operator of the form $$L(u)=-\textrm{div} (a(x)\nabla u)$$ and a suitable nonlinearity $f$. The function $a$ vanishes on smooth 1-codimensional submanifolds of $\Omega$ where it is not allowed to be $C^{2}$. By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where $a$ vanishes.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f03d3d7f20c45e27d94ff3007229112 https://doi.org/10.3233/asy-211728 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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