Gradient estimates for nonlinear equations with measurable nonlinearities from composite material

초록

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 W1,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. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

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