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On a localization-in-frequency approach for a class of elliptic problems with singular boundary data

Part of: Partial differential equations Elliptic equations and systems Miscellaneous topics - Partial differential equations Harmonic analysis in several variables Representations of solutions

Published online by Cambridge University Press:  21 May 2024

Lucas C. F. Ferreira  and
Wender S. Lagoin
Lucas C. F. Ferreira
Affiliation:
IMECC-Department of Mathematics, State University of Campinas, Rua Sérgio Buarque de Holanda, 651, CEP 13083-859, Campinas, SP, Brazil (lcff@ime.unicamp.br; wendertnb@gmail.com)
Wender S. Lagoin
Affiliation:
IMECC-Department of Mathematics, State University of Campinas, Rua Sérgio Buarque de Holanda, 651, CEP 13083-859, Campinas, SP, Brazil (lcff@ime.unicamp.br; wendertnb@gmail.com)
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Abstract

We consider a class of nonhomogeneous elliptic equations in the half-space with critical singular boundary potentials and nonlinear fractional derivative terms. The forcing terms are considered on the boundary and can be taken as singular measure. Employing a functional setting and approach based on localization-in-frequency and Littlewood–Paley decomposition, we obtain results on solvability, regularity, and symmetry of solutions.

Keywords

nonlinear elliptic boundary value problemslocalization-in-frequency techniquesLittlewood–Paley decompositionsolvabilitysymmetrysingular potentialsmeasure data

MSC classification

Primary: 35J66: Nonlinear boundary value problems for nonlinear elliptic equations
Secondary: 35J75: Singular elliptic equations 35A22: Transform methods (e.g. integral transforms) 35C15: Integral representations of solutions 35B07: Axially symmetric solutions 35R06: Partial differential equations with measure 42B37: Harmonic analysis and PDE
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 35
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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