@misc{10481/103463,
year = {2024},
month = {7},
url = {https://hdl.handle.net/10481/103463},
abstract = {In this paper we consider a doubly critical nonlinear elliptic problem
with Neumann boundary conditions. The existence of blow-up solutions for this
problem is related to the blow-up analysis of the classical geometric problem
of prescribing negative scalar curvature K = −1 on a domain of Rn and mean
curvature H = D(n(n − 1))−1/2, for some constant D > 1, on its boundary, via a
conformal change of the metric. Assuming that n ≥ 6 and D > √(n + 1)/(n − 1),
we establish the existence of a positive solution which concentrates around an
elliptic boundary point which is a nondegenerate critical point of the original
mean curvature.},
organization = {Spanish Ministry of Universities},
organization = {Next Generation EU},
organization = {Margarita Salas, University of Granada},
organization = {FEDER-MINECO  PID2021-122122NB-I00},
organization = {Junta of Andalucia (FQM-116)},
organization = {INAM-GNAMPA  CUP_E55F22000270001},
publisher = {Springer Nature},
keywords = {Nonlinear elliptic equations},
keywords = {Critical Sobolev exponents},
keywords = {Blow-up solutions},
title = {The role of the boundary in the existence of blow-up solutions for a doubly critical elliptic problem},
doi = {10.1007/s00030-025-01042-w},
author = {Cruz-Blázquez, Sergio},
}