Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing

2024/10/01 by Goro Akagi, Akagi, Goro, Hiroki Miyakawa +1
Engineering · Mathematics · #35J57 #35J92 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2410.00585

openalex publication_date 2024/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of p-Laplacian type with absorption and (prescribed) locally integrable forcing posed in (possibly unbounded) Lipschitz domains. In particular, the forcing terms may not belong to the dual space of an energy space, e.g., W^1,p_{\rm loc}, which is necessary for the existence of weak (or energy) solutions of class W^1,p_{\rm loc}. The method of a proof relies on both local energy estimates and a relative truncation technique developed by Bulíček and Schwarzacher (Calc. Var. PDEs in 2016), where the bounded domain case is studied for (globally) integrable forcing.

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