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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 5, October 2016
  4. On uniform estimates for Laplace equation in balls with small holes
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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
Generic uniqueness of shortest closed geodesics
Infinitely many nonlocal conservation laws for the ABC equation with $$A+B+C\ne 0$$
Multiple solutions of the $$L_{p}$$ -Minkowski problem
On curvature pinching of conic 2-spheres
Transport equations with integral terms: existence, uniqueness and stability
Regularity of a class of non-uniformly nonlinear elliptic equations
Dynamics of optimal partial transport
On uniform estimates for Laplace equation in balls with small holes
On the Hopf–Oleinik lemma for degenerate-elliptic equations at characteristic points
Lusin approximation for horizontal curves in step 2 Carnot groups
Metric measure spaces supporting Gagliardo–Nirenberg inequalities: volume non-collapsing and rigidities
Global weighted estimates for the nonlinear parabolic equations with non-standard growth
Ground states of a ternary system including attractive and repulsive Coulomb-type interactions
Instantons and singularities in the Yang–Mills flow
Stability of point defects of degree $$\pm \frac{1}{2}$$ in a two-dimensional nematic liquid crystal model
Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids
$$L^p$$ -spectrum of the Dirac operator on products with hyperbolic spaces
Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory
On the shape of capillarity droplets in a container
Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients
Convergence of the thresholding scheme for multi-phase mean-curvature flow
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
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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On uniform estimates for Laplace equation in balls with small holes

Content Provider SpringerLink
Author Lu, Yong
Copyright Year 2016
Abstract In this paper, we consider the Dirichlet problem of the three-dimensional Laplace equation in the unit ball with a shrinking hole. The problem typically arises from homogenization problems in domains perforated with tiny holes. We give an almost complete description concerning the uniform $$W^{1,p}$$ estimates: for any $$3/2
Ending Page 19
Page Count 19
Starting Page 1
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 5
Volume Number 55
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2016-09-20
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Homogenization; equations in media with periodic structure Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 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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