The role of the mean curvature in semilinear Neumann problem involving critical exponent. (English) Zbl 0847.35047

A Neumann problem involving a right-hand side with critical Sobolev exponent is considered in a bounded domain \(D\) in \(\mathbb{R}^n\). For a space dimension \(n\geq 6\), an existence theorem is given for a solution concentrating at a non-degenerate point of the mean curvature of the boundary of \(D\). A similar procedure was used in [O. Rey, J. Funct. Anal. 89, No. 1, 1-52 (1990; Zbl 0786.35059)]. The limit of the energy is given in terms of the best Sobolev constant, which is defined using a maximization problem with constraints.


35J65 Nonlinear boundary value problems for linear elliptic equations


Zbl 0786.35059
Full Text: DOI


[1] Adimurthi and Mancini, G. 1991.A tribute in honour of G. Prodi, Edited by: Ambrosetti, Marino and Scoula, Norm. 9–25. Sup. Pisa.
[2] DOI: 10.1006/jfan.1993.1053 · Zbl 0793.35033
[3] Adimurthi, Filomena, Pacella and Yadava, S.L. Characterization of concentration points and Lestimates for solutions of semilinear Neumann problem involving critical Sobolev exponents. Diflerential and Integral equations. to appear · Zbl 0814.35029
[4] DOI: 10.1016/0022-1236(91)90099-Q · Zbl 0755.46014
[5] DOI: 10.1016/0022-1236(90)90002-3 · Zbl 0786.35059
[6] DOI: 10.1016/0022-0396(91)90014-Z · Zbl 0766.35017
[7] Wang, Z.Q., Remarks on a non linear Neumann problem with crit- ical exponent, preprint.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.