Prescribing singularities of weak solutions of a nonlinear elliptic system in the plane

Inspired by Frehse’s (Math Z 134 (10):229–230, 1973) work, we show that his elliptic system $$\Delta u = F(u, \nabla u)$$ in the plane has bounded weak solutions u with arbitrarily prescribed singular sets.

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Publication Details

Journal
Mathematische Zeitschrift
Published
2025-09-16
DOI
https://doi.org/10.1007/s00209-025-03851-2
Primary Topic
Differential Equations and Boundary Problems
Type
article
Field-Weighted Citation Impact
0.00
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article

Prescribing singularities of weak solutions of a nonlinear elliptic system in the plane

Bogdan Petraszczuk
Mathematische Zeitschrift
Differential Equations and Boundary Problems
article

Prescribing singularities of weak solutions of a nonlinear elliptic system in the plane

Bogdan Petraszczuk
article en

Abstract

Inspired by Frehse’s (Math Z 134 (10):229–230, 1973) work, we show that his elliptic system $$\Delta u = F(u, \nabla u)$$ in the plane has bounded weak solutions u with arbitrarily prescribed singular sets.

Mathematische ZeitschriftVol. 311(3)
Warsaw School of Computer Science (PL)
Openalex Percentile: Top 64%
Differential Equations and Boundary Problems
DOIOpen Access PDFOpenAlex
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Prescribing singularities of weak solutions of a nonlinear elliptic system in the plane — Bogdan Petraszczuk · Mathematische Zeitschrift (2025) | TGRS Research Map | TGRS