In this paper we study the Poisson problem, {−div(dβ∇u)=finΩu=0on∂Ω, where Ω⊂RN, N≥2 is a smooth bounded domain, f is a continuous function, β<1, and d(x)=dist(x,∂Ω). We describe the behaviour of u near ∂Ω and discuss some of its regularity properties.
Low regularity results for degenerate Poisson problems / M. Calanchi, M. Grossi. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 443:(2025 Oct 25), pp. 113567.1-113567.12. [10.1016/j.jde.2025.113567]
Low regularity results for degenerate Poisson problems
M. CalanchiPrimo
;
2025
Abstract
In this paper we study the Poisson problem, {−div(dβ∇u)=finΩu=0on∂Ω, where Ω⊂RN, N≥2 is a smooth bounded domain, f is a continuous function, β<1, and d(x)=dist(x,∂Ω). We describe the behaviour of u near ∂Ω and discuss some of its regularity properties.
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