Critical points of the Moser-Trudinger functional on closed surfaces

• 成果类型: Article
• 署名作者: De Marchis, Francesca; Malchiodi, Andrea; Martinazzi, Luca; Thizy, Pierre-Damien
• 署名单位: Sapienza University Rome; Scuola Normale Superiore di Pisa; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01142-9
• 发表日期: 2022
• 页码: 1165-1248
• 关键词: mean-field equation; bubbling solutions; existence result; INEQUALITY; profile

摘要

Given a closed Riemann surface (Sigma, g(0)) and any positive weight f is an element of C-infinity(Sigma), we use a minmax scheme together with compactness, quantization results and with sharp energy estimates to prove the existence of positive critical points of the functional I-p,I-beta(u) = 2 - p/2 (p parallel to u parallel to(2)(H1)/2 beta) p/2-p - in integral(Sigma)(e(up-) - 1) f d v(g0), for every p is an element of (1, 2) and beta > 0, or for p = 1 and beta is an element of (0, infinity) \4 pi N. Letting p up arrow 2 we obtain positive critical points of the Moser-Trudinger functional F(u) := integral(Sigma)(e(u2) - 1)f dv(g0) constrained to epsilon(beta) := {v s.t. parallel to v parallel to(2)(H1) = beta} for any beta > 0.