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 functionalI-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 functionalF(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.
Critical points of the Moser-Trudinger functional on closed surfaces / De Marchis, F; Malchiodi, A; Martinazzi, L; Thizy, Pd. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 230:3(2022), pp. 1165-1248. [10.1007/s00222-022-01142-9]
Critical points of the Moser-Trudinger functional on closed surfaces
De Marchis, F;Martinazzi, L;
2022
Abstract
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 functionalI-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 functionalF(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.File | Dimensione | Formato | |
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