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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 53
  3. Calculus of Variations and Partial Differential Equations : Volume 53, Issue 3-4, July 2015
  4. Convexity estimates for the Green’s function
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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 53, Issue 3-4, July 2015
Liouville type results for local minimizers of the micromagnetic energy
On the derivation of homogenized bending plate model
A uniform Poincaré estimate for quadratic differentials on closed surfaces
Geometric gradient estimates for solutions to degenerate elliptic equations
On monotonicity of some functionals under rearrangements
Some smoothness results for the optimal design of a two-composite material which minimizes the energy
Convexity estimates for the Green’s function
On existence and phase separation of solitary waves for nonlinear Schrödinger systems modelling simultaneous cooperation and competition
Homogenization of the nonlinear bending theory for plates
Removable sets for Lipschitz harmonic functions on Carnot groups
Weak perturbations of the p-Laplacian
Riesz potential estimates for a general class of quasilinear equations
Structure of extremals of variational problems in the regions close to the endpoints
Positive ground states for a system of Schrödinger equations with critically growing nonlinearities
Quantization for an elliptic equation with critical exponential growth on compact Riemannian surface without boundary
Reifenberg flatness of free boundaries in obstacle problems with VMO ingredients
Weighted quasilinear eigenvalue problems in exterior domains
Improved energy bounds for Schrödinger operators
Three-spheres theorem for $$p$$ -harmonic mappings
Calculus of Variations and Partial Differential Equations : Volume 53, Issue 1-2, May 2015
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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Convexity estimates for the Green’s function

Content Provider SpringerLink
Author Shi, Shujun
Copyright Year 2014
Abstract In this paper, for the Green’s function of a bounded convex domain $$\Omega $$ with pole at $$x_0\in \Omega $$ , we find the auxiliary curvature function which satisfies a differential inequality and so attains its minimum on the boundary. Moreover, we obtain a convexity estimate for the Green’s function of the domain above and give the proof of its specific convexity from the viewpoint of partial differential equations themselves.
Ending Page 688
Page Count 14
Starting Page 675
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 53
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2014-08-12
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Dependence of solutions on initial and boundary data, parameters Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation Convexity properties Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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