On a smoothly bounded domain Omega subset of R(2m) we consider a sequence of positive solutions u(k) ->(omega) 0 in H(m)(Omega) to the equation (-Delta)(m)u(k) = lambda(k)u(k)e(mu2k) subject to Dirichlet boundary conditions, where 0 < lambda(k) -> 0. Assuming that 0 < Lambda := lim(k ->infinity) integral(Omega) u(k)(-Delta)(m) u(k)dx < infinity, we prove that Lambda is an integer multiple of Lambda(1) := (2m - 1)! vol(S(2m)), the total Q-curvature of the standard 2m-dimensional sphere.
Quantization for an elliptic equation of order 2m with critical exponential non-linearity / Martinazzi, Luca; Struwe, Michael. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 270:1-2(2012), pp. 453-486. [10.1007/s00209-010-0807-1]
Quantization for an elliptic equation of order 2m with critical exponential non-linearity
Martinazzi, Luca;
2012
Abstract
On a smoothly bounded domain Omega subset of R(2m) we consider a sequence of positive solutions u(k) ->(omega) 0 in H(m)(Omega) to the equation (-Delta)(m)u(k) = lambda(k)u(k)e(mu2k) subject to Dirichlet boundary conditions, where 0 < lambda(k) -> 0. Assuming that 0 < Lambda := lim(k ->infinity) integral(Omega) u(k)(-Delta)(m) u(k)dx < infinity, we prove that Lambda is an integer multiple of Lambda(1) := (2m - 1)! vol(S(2m)), the total Q-curvature of the standard 2m-dimensional sphere.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
