Elliptic equations of fourth-order with critical exponents on compact Riemannian manifolds

DOI10.1016/S0021-7824(01)01212-0zbMath1031.58010MaRDI QIDQ1606258

Daniela Caraffa

Publication date: 24 July 2002

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

elliptic equations with critical Sobolev exponentnonlinear analysis on manifoldsSobolev spaces and inequalities

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05)

Related Items (13)

Multiple solutions to singular fourth order elliptic equations on compact manifolds ⋮ Multiplicity of solutions for a fourth order elliptic equation with critical exponent on compact manifolds ⋮ Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds ⋮ On the singular second-order elliptic equation ⋮ Nodal solutions for a Paneitz-Branson type equation ⋮ Best constants in second-order Sobolev inequalities on Riemannian manifolds and applications. ⋮ Nonlinear elliptic fourth order equations existence and multiplicity results ⋮ Study of nonlinear elliptic problems of fourth order with critical exponents on compact Riemannian manifolds ⋮ On a fourth order Lichnerowicz type equation involving the Paneitz-Branson operator ⋮ Some properties of the Paneitz operator and nodal solutions to elliptic equations ⋮ Harnack inequalities for elliptic operators of order 2 and 4, and concentration phenomena. ⋮ Nonhomogeneous polyharmonic elliptic problems involving GJMS operator on Riemannian manifold ⋮ Best constant in critical Sobolev inequalities of second-order in the presence of symmetries

Cites Work

• The concentration-compactness principle in the calculus of variations. The limit case. I
• Variational identities and applications to differential systems
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Problèmes isoperimetriques et espaces de Sobolev
• Critical exponents, critical dimensions and the biharmonic operator
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Existence and non-existence results for semilinear elliptic problems in unbounded domains
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