Browsing by Author "Pacard, Frank"
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- ItemBoundary singularities for weak solutions of semilinear elliptic problems(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) del Pino, Manuel; Musso, Monica; Pacard, FrankLet Omega be a bounded domain in R-N, N >= 2, with smooth boundary partial derivative Omega. We construct positive weak solutions of the problem Delta u + u(p) = 0 in Omega, which vanish in a suitable trace sense on partial derivative Omega, but which are singular at prescribed isolated points if p is equal or slightly above N+1/N-1. Similar constructions are carried out for solutions which are singular at any given embedded submanifold of partial derivative Omega of dimension k epsilon [0, N -2], if p equals or it is slightly above N-k-1/N-k-1, and even on countable families of these objects, dense on a given closed set. The role of the exponent N+1/N-1 (first discovered by Brezis and Turner [H. Brezis, R. Turner, N-1 On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977) 601-614]) for boundary regularity, parallels that of N/N-2 for interior singularities. (c) 2007 Elsevier Inc. All rights reserved.
- ItemBubbling along boundary geodesic near the second critical exponent(2010) Pino, Manuel del; Musso Polla, Mónica; Pacard, Frank
- ItemFinite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation(2012) Musso Polla, Mónica; Pacard, Frank; Wei, Juncheng
- ItemLarge energy entire solutions for the Yamabe equation(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011) del Pino, Manuel; Musso, Monica; Pacard, Frank; Pistoia, AngelaWe consider the Yamabe equation Delta u + n(n-2_/4 vertical bar u vertical bar 4/n-2 u = 0 in R(n), n >= 3. Let k >= 1 and xi(k)(j) = (e(2j pi u/k), 0) is an element of R(n) = C x R(n-2). For all large k we find a solution of the form u(k)(x)= u(x) - Sigma(k)(j=1) mu(k) (-n-2/2) U X (mu(-1)(k) (x - xi(j)) +o(1), where U(x) = (2/1+vertical bar x vertical bar(2)) (n-2/2), mu(k) = c(n)/k(2) for n >= 4, mu k = c/k(2)(logk)(2) for n =3 and o(1) -> 0 uniformly as k -> +infinity. (C) 2011 Elsevier Inc. All rights reserved.
- ItemSolutions without any symmetry for semilinear elliptic problems(2016) Weiwei, Ao; Musso Polla, Mónica; Pacard, Frank; Wei, Juncheg
- ItemTorus action on S^n and sign changing solutions for conformally invariant equations(2013) Del Pino, Manuel; Musso Polla, Mónica; Pacard, Frank; Pistoia, Angela