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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
Full Text: DOI
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