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Renormalized Solutions for Nonlinear and Non-Coercive Elliptic Problems Involving Hardy Potentials and L1-Data
Soluciones renormalizadas para problemas elípticos no lineales y no coercitivos que involucran potenciales Hardy y funciones de tipo L1
DOI:
https://doi.org/10.15446/recolma.v59n2.125949Palabras clave:
Anisotropic Sobolev spaces, strongly nonlinear elliptic equation, non-coercive problems, renormalized solutions (en)Espacios anisotrópicos de Sobolev, ecuaciones elípticas fuertemente no lineales, problemas no coercitivos, soluciones renormalizadas (es)
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This work is centered around the study of the following noncoercive elliptic problem:
Au + g(x, u,∇u) = f(x) + |u|p0−2 u/|x|p0 in Ω,
u = 0 on ∂Ω,
In the anisotropic Sobolev space, where Ω is a bounded open subset of RN (N ≥ 2) that includes the origin, with g(x, s, ξ) subject to certain growth conditions and f ∈ L1(Ω). We prove the existence of renormalized solutions for the strongly nonlinear and non-coercive elliptic Dirichlet problem. Furthermore, we establish several regularity results.
Este trabajo se centra en el estudio del siguiente problema coercitivo elíptico:
Au + g(x, u,∇u) = f(x) + |u|p0−2 u/|x|p0 in Ω,
u = 0 on ∂Ω,
en un espacio anisotrópico de Sobolev, donde Ω es un subconjunto abierto acotado de RN (N ≥ 2) que incluye el origen, donde g(x, s, ξ) está sujeto a restricciones relacionadas a su crecimiento y f ∈ L1(Ω). Probamos la existencia de soluciones renormalizadas para el problema elíptico de Dirichlet. Más aún, probamos varios resultados acerca de la regularidad de las soluciones.
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