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Existence of solutions for some degenerate elliptic equation under Fourier boundary conditions
Existencia de soluciones para alguna ecuación elíptica degenerada en condiciones de contorno de Fourier
DOI:
https://doi.org/10.15446/recolma.v59n1.122852Palabras clave:
Anisotropic variable exponent Sobolev space, quasilinear elliptic problem, Hardy potential, Fourier boundary conditions, renormalized solution, L1-data (en)Espacio de Sobolev de exponente variable anisotrópico, problema elíptico cuasilineal, potencial de Hardy, condiciones de contorno de Fourier, solución renormalizada, L1-datos (es)
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This paper aims to study the existence of renormalized solutions for the anisotropic elliptic problem with a Hardy potential and Fourier boundary conditions
−ΣNi=1 Di ai(x, u, ∇u) + α|u|r(x) - 1 u = ν |u|p0(x)−2u /|x|p0(x) + f(x) in Ω,
ΣNi=1 ai(x, u, ∇u) · ni + λu = g(x) on ∂Ω,
where Ω is an open bounded subset of RN (N ≥ 2), the data f belongs to L1(Ω), g ∈ L1(∂Ω) and α, λ, ν > 0. with ai(x, s, ξ) are Carath´eodory functions that verifying some nonstandard conditions.
Este artículo tiene como objetivo estudiar la existencia de soluciones renormalizadas para el problema elíptico anisotrópico con un potencial de Hardy y condiciones de borde de Fourier
−ΣNi=1 Di ai(x, u, ∇u) + α|u|r(x) - 1 u = ν |u|p0(x)−2u /|x|p0(x) + f(x) in Ω,
ΣNi=1 ai(x, u, ∇u) · ni + λu = g(x) on ∂Ω,
donde Ω es un subconjunto abierto y acotado de RN (N ≥ 2), los datos f pertenecen a L1(Ω), g ∈ L1(∂Ω) y α, λ, ν > 0. con ai(x, s, ξ) son funciones de Carathéodoria que verifican algunas condiciones no estándar.
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