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Mixed boundary value problems for nonlinear elliptic equations in multidimensional non‐smooth domains
Author(s) -
Ebmeyer Carsten,
Frehse Jens
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.1999.3212030104
Subject(s) - mathematics , boundary value problem , nonlinear system , mathematical analysis , piecewise , boundary (topology) , elliptic curve , boundary values , pure mathematics , physics , quantum mechanics
The nonlinear elliptic equation\documentclass{article}\pagestyle{empty}\begin{document}$$ ‐ \sum\limits_{i = 1}^n {\partial _i F_i \left({x,\nabla _u} \right)} = f\left(x \right) + \sum\limits_{i = 1}^n {\partial _i f_i \left(x \right)} $$\end{document}is investigated. It is supposed that u fulfils a mixed boundary value condition and that Ω ⊂ IR n (n ≥ 3) has a piecewise smooth boundary. W s,2 — regularity (s < 3/2) of u and L p — properties of the first and the second derivatives of u are proven.