Solutions with high dimensional singular set, to a conformally invariant elliptic equation in \(\mathbb{R}^ 4\) and in \(\mathbb{R}^ 6\)

DOI10.1007/BF02102645zbMath0822.35052OpenAlexW2077720248MaRDI QIDQ1315026

Frank Pacard

Publication date: 9 October 1995

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02102645

zbMATH Keywords

semilinear elliptic equationpositive solution with prescribed singular set

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20)

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Cites Work

• On a conformally invariant elliptic equation on \(R^ n\)
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Conformally flat metrics of constant positive scalar curvature on subdomains of the sphere
• Remarks on the Schrödinger operator with singular complex potentials
• Existence and convergence of positive weak solutions of \(-\Delta u=u^{n\over {n-2}}\) in bounded domains of \(\mathbb{R}^ n\), \(n\geq 3\)
• Local behavior of solutions of some elliptic equations
• The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation
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