Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590076 | Journal of Functional Analysis | 2017 | 23 Pages |
Abstract
We give new criteria for the existence of weak solutions to an equation with a super linear source term−Δu=uqin Ω,u=σon ∂Ω where Ω is either a bounded smooth domain or R+N, q>1q>1 and σ∈M+(∂Ω)σ∈M+(∂Ω) is a nonnegative Radon measure on ∂Ω. One of the criteria we obtain is expressed in terms of some Bessel capacities on ∂Ω. We also give a sufficient condition for the existence of weak solutions to equation with source mixed terms.−Δu=|u|q1−1u|∇u|q2in Ω,u=σon ∂Ω where q1,q2≥0q1,q2≥0, q1+q2>1q1+q2>1, q2<2q2<2, σ∈M(∂Ω)σ∈M(∂Ω) is a Radon measure on ∂Ω.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marie-Françoise Bidaut-Véron, Giang Hoang, Quoc-Hung Nguyen, Laurent Véron,