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Gradient estimates for nonlinear equations with measurable nonlinearities from composite material.

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Title: Gradient estimates for nonlinear equations with measurable nonlinearities from composite material.
Authors: Jang, Yunsoo1 (AUTHOR) yunsoojang@kangwon.ac.kr
Source: Calculus of Variations & Partial Differential Equations. Jun2025, Vol. 64 Issue 5, p1-22. 22p.
Subject Terms: *COMPOSITE materials, *ENGINEERING mathematics, *NONLINEAR equations, *COMPOSITE structures, *NONLINEAR theories
Abstract: We study the Calderón-Zygmund theory for nonlinear p-Laplacian type elliptic equations from composite material. We assume that the composite material is composed of several subdomains in the whole domain and the associated measurable nonlinearity under consideration is locally merely measurable in a variable but has small bounded mean oscillation in the other variables in each subdomain. From the relation between the internal geometry of composite material and measurable nonlinearities, we establish global W 1 , q estimates for p ≤ q < ∞ and as a corollary, we obtain the minimal regularity requirements of Calderón-Zygmund estimates for p-Laplacian type elliptic equations from the internal structure of composite material. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:We study the Calderón-Zygmund theory for nonlinear p-Laplacian type elliptic equations from composite material. We assume that the composite material is composed of several subdomains in the whole domain and the associated measurable nonlinearity under consideration is locally merely measurable in a variable but has small bounded mean oscillation in the other variables in each subdomain. From the relation between the internal geometry of composite material and measurable nonlinearities, we establish global W 1 , q estimates for p ≤ q < ∞ and as a corollary, we obtain the minimal regularity requirements of Calderón-Zygmund estimates for p-Laplacian type elliptic equations from the internal structure of composite material. [ABSTRACT FROM AUTHOR]
ISSN:09442669
DOI:10.1007/s00526-025-03008-3