On some conjectures proposed by Haïm Brezis.

DOI10.1016/j.na.2003.10.012zbMath1134.35045OpenAlexW2132777815WikidataQ123201268 ScholiaQ123201268MaRDI QIDQ1426421

Pierpaolo Esposito

Publication date: 14 March 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.10.012

zbMATH Keywords

critical Sobolev exponentelliptic problemlow-dimension phenomena

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60)

Related Items (5)

Energy asymptotics in the three-dimensional Brezis-Nirenberg problem ⋮ The quasi-linear Brezis-Nirenberg problem in low dimensions ⋮ Positive solutions of the Gross–Pitaevskii equation for energy critical and supercritical nonlinearities ⋮ Critical functions and blow-up asymptotics for the fractional Brezis-Nirenberg problem in low dimension ⋮ Sign-changing solutions for critical equations with Hardy potential

Cites Work

• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Elliptic equations with critical Sobolev exponents in dimension 3
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: the radial case. II
• The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
• Elliptic equations with critical exponent on spherical caps of \(S^{3}\)
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Optimal Sobolev inequalities and extremal functions. The three dimensional case
• Asymptotic behavior of positive solutions of quasilinear elliptic equations with critical Sobolev growth
• Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: the radial case.
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