2023/10/16 by Ayana Pinheiro de Castro Santana, Santana, Ayana Pinheiro de Castro, Luís Henrique de Miranda +1 · 1 citation
Computer Science · Mathematics · #35B65 #35D99 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2310.10194
openalex publication_date 2023/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the existence and regularity of weak solutions for the following system \begincases -div(M(x)∇ u) + g(x,u,v) = f in Ω
-div(M(x)∇ v) = h(x,u,v) in Ω
u=v=0 on ∂ Ω, \endcases where Ω is an open bounded subset of ℝN, for N>2, f∈ Lm(Ω), where m>1 and h, g are two Carathéodory functions. We prove that under appropriate conditions on g and h there exist solutions which escape the predicted regularity by the classical Stampacchia's theory causing the so-called regularizing effect.