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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 48
  3. Calculus of Variations and Partial Differential Equations : Volume 48, Issue 1-2, September 2013
  4. Capacitary estimates of solutions of semilinear parabolic equations
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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 48, Issue 3-4, November 2013
Calculus of Variations and Partial Differential Equations : Volume 48, Issue 1-2, September 2013
Geodesic convexity of the relative entropy in reversible Markov chains
Regularity of nonlocal minimal cones in dimension 2
Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds
Geometric relative Hardy inequalities and the discrete spectrum of Schrödinger operators on manifolds
Lions-type compactness and Rubik actions on the Heisenberg group
Symplectic mean curvature flow in CP 2
Capacitary estimates of solutions of semilinear parabolic equations
The von Kármán theory for incompressible elastic shells
Kinks in two-phase lipid bilayer membranes
Existence and concentration of positive solutions for semilinear Schrödinger–Poisson systems in $${\mathbb{R}^{3}}$$
Erratum to: Existence and concentration of positive solutions for semilinear Schrödinger–Poisson systems in $${\mathbb{R}^{3}}$$
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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Capacitary estimates of solutions of semilinear parabolic equations

Content Provider SpringerLink
Author Marcus, Moshe Veron, Laurent
Copyright Year 2012
Abstract We prove that any positive solution of $${\partial_tu-\Delta u+u^q=0 (q > 1)}$$ in $${\mathbb{R}^N \times (0, \infty)}$$ with initial trace (F, 0), where F is a closed subset of $${\mathbb{R}^{N}}$$ can be represented, up to two universal multiplicative constants, by a series involving the Bessel capacity $${C_{2/q, q^{\prime}}}$$ . As a consequence we prove that there exists a unique positive solution of the equation with such an initial trace. We also characterize the blow-up set of u(x, t) when $${t \downarrow 0}$$ , by using the “density” of F expressed in terms of the $${C_{2/q, q^{\prime}}}$$ -Bessel capacity.
Ending Page 183
Page Count 53
Starting Page 131
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 1-2
Volume Number 48
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2012-08-21
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Fine potential theory Heat equation Potentials and capacities Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Integral representations, integral operators, integral equations methods Nonlinear parabolic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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