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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 41
  3. Calculus of Variations and Partial Differential Equations : Volume 41, Issue 3-4, July 2011
  4. Nonlinear elliptic problems with a singular weight on the boundary
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 41, Issue 3-4, July 2011
Adjoint methods for static Hamilton–Jacobi equations
On the entire self-shrinking solutions to Lagrangian mean curvature flow
A compactness theorem for scalar-flat metrics on manifolds with boundary
Area minimization among marginally trapped surfaces in Lorentz–Minkowski space
Two-phase semilinear free boundary problem with a degenerate phase
Continuity of solutions of a problem in the calculus of variations
Solutions with many mixed positive and negative interior spikes for a semilinear Neumann problem
Conformal metrics with prescribed Q-curvature on S n
Some inequalities related to Sobolev norms
An approach to minimization under a constraint: the added mass technique
2π-periodic self-similar solutions for the anisotropic affine curve shortening problem
Nonlinear elliptic problems with a singular weight on the boundary
Calculus of Variations and Partial Differential Equations : Volume 41, Issue 1-2, May 2011
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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Nonlinear elliptic problems with a singular weight on the boundary

Content Provider SpringerLink
Author Dávila, Juan Peral, Ireneo
Copyright Year 2010
Abstract 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.
Ending Page 586
Page Count 20
Starting Page 567
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 41
Language English
Publisher Springer-Verlag
Publisher Date 2010-10-14
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems Boundary value problems for second-order elliptic equations Spaces of measurable functions ( $L^p$ -spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Variational methods for second-order elliptic equations Degenerate elliptic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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