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arXiv · 2512.18742

Non-homogeneous conormal derivative problem for quasilinear elliptic equations with Morrey data

Dian K. Palagachev·Lubomira G. Softova
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Abstract

A non-homogeneous conormal derivative problem is considered for quasilinear divergence form elliptic equations modeled on the $m$-Laplacian operator. The nonlinear terms are given by Carath\'eodory functions and satisfy controlled growth structure conditions with respect to the solution and its gradient, while their $x$-behaviour is controlled in terms of suitable Morrey spaces. Global essential boundedness is proved for the weak solutions, generalizing thus the classical $L^p$-result of Ladyzhenskaya and Ural'tseva to the framework of the Morrey scales.

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Dian K. Palagachev, Lubomira G. Softova. 2025-12-21. Non-homogeneous conormal derivative problem for quasilinear elliptic equations with Morrey data. https://arxiv.org/abs/2512.18742

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