caa a22 4500 445843284 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s00526-010-0376-5 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0376-5 Nonlinear elliptic problems with a singular weight on the boundary [Elektronische Daten] [Juan Dávila, Ireneo Peral] We study existence of solutions to $$-\Delta u = \frac{u^p}{|x|^2}\quad u\, >\,0 \,{\rm in }\,\Omega$$with u=0 on ∂Ω, where Ω is a smooth bounded domain in $${\mathbb {R}^N}$$ , N≥ 3 with $${0\,\in\,\partial \Omega}$$ and $${1< p < \frac{N+2}{N-2}}$$ . The existence of solutions depends on the geometry of the domain. On one hand, if the domain is starshaped with respect to the origin there are no energy solutions. On the other hand, in dumbbell domains via a perturbation argument, the equation has solutions. Springer-Verlag, 2010 Dávila Juan Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile aut Peral Ireneo Departamento de Matemáticas, Universidad Autónoma de Madrid-ICMAT, 28049, Madrid, Spain aut Calculus of Variations and Partial Differential Equations Springer-Verlag 41/3-4(2011-07-01), 567-586 0944-2669 41:3-4<567 2011 41 526 https://doi.org/10.1007/s00526-010-0376-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0376-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dávila Juan Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile aut NATIONALLICENCE 700 1- Peral Ireneo Departamento de Matemáticas, Universidad Autónoma de Madrid-ICMAT, 28049, Madrid, Spain aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 41/3-4(2011-07-01), 567-586 0944-2669 41:3-4<567 2011 41 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer