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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 55
  3. Calculus of Variations and Partial Differential Equations : Volume 55, Issue 2, April 2016
  4. Existence and non existence results for the singular Nirenberg problem
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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 55, Issue 6, December 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 5, October 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 4, August 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 3, June 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 2, April 2016
A spectral condition for Liouville-type result of monostable KPP equation in periodic shear flows
Some sharp Hodge Laplacian and Steklov eigenvalue estimates for differential forms
Isolated singularities of positive solutions to the weighted p-Laplacian
Partial Hölder regularity of the steady fractional Navier–Stokes equations
Global dynamics of the Lotka–Volterra competition–diffusion system with equal amount of total resources, II
Limits of elastic models of converging Riemannian manifolds
Mirror symmetric solutions to the centro-affine Minkowski problem
Stability of the Camassa-Holm peakons in the dynamics of a shallow-water-type system
Solutions to the Einstein-scalar field constraint equations with a small TT-tensor
A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation
Generalized solutions of a kinetic granular media equation by a gradient flow approach
Local solutions to a free boundary problem for the Willmore functional
The positive mass theorem for multiple rotating charged black holes
Gradient estimates for elliptic equations with $$L^{p(\cdot )}\log L$$ growth
Regularity at the free boundary for Dirac-harmonic maps from surfaces
Optimal decay of extremals for the fractional Sobolev inequality
Existence and non existence results for the singular Nirenberg problem
Random homogenization of coercive Hamilton–Jacobi equations in 1d
Noether-like theorems for causal variational principles
Uniqueness and nondegeneracy of positive radial solutions of $$\mathbf {div\,{\varvec{(}}{\varvec{\rho }} \nabla u{\varvec{)}} +{\varvec{\rho }}{\varvec{(}}-gu+hu^p{\varvec{)}}=0}$$
Elliptic bindings for dynamically convex Reeb flows on the real projective three-space
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 1, February 2016
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 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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Existence and non existence results for the singular Nirenberg problem

Content Provider SpringerLink
Author De Marchis, Francesca López Soria, Rafael
Copyright Year 2016
Abstract In this paper we study the problem, posed by Troyanov (Trans AMS 324: 793–821, 1991), of prescribing the Gaussian curvature under a conformal change of the metric on surfaces with conical singularities. Such geometrical problem can be reduced to the solvability of a nonlinear PDE with exponential type non-linearity admitting a variational structure. In particular, we are concerned with the case where the prescribed function K changes sign. When the surface is the standard sphere, namely for the singular Nirenberg problem, we give sufficient conditions on K, concerning mainly the regularity of its nodal line and the topology of its positive nodal region, to be the Gaussian curvature of a conformal metric with assigned conical singularities. Besides, we find a class of functions on $$\mathbb {S}^2$$ which do not verify our conditions and which can not be realized as the Gaussian curvature of any conformal metric with one conical singularity. This shows that our result is somehow sharp.
Ending Page 35
Page Count 35
Starting Page 1
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 2
Volume Number 55
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2016-03-26
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx] Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Variational methods for second-order elliptic equations Conformal differential geometry
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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