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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 44
  3. Calculus of Variations and Partial Differential Equations : Volume 44, Issue 3-4, July 2012
  4. Entropy method for line-energies
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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 44, Issue 3-4, July 2012
Volume-constrained minimizers for the prescribed curvature problem in periodic media
Weak KAM Theory topics in the stationary ergodic setting
Heat kernels of two-dimensional magnetic Schrödinger and Pauli operators
Entropy method for line-energies
Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction
On the characterization of the compact embedding of Sobolev spaces
Local Poincaré inequalities from stable curvature conditions on metric spaces
Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution
Beyond the Trudinger-Moser supremum
The geometric Neumann problem for the Liouville equation
Partial regularity of stable solutions to the Emden equation
Calculus of Variations and Partial Differential Equations : Volume 44, Issue 1-2, May 2012
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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Entropy method for line-energies

Content Provider SpringerLink
Author Merlet, Beît Ignat, Radu
Copyright Year 2011
Abstract In this paper we analyze energy functionals concentrated on the discontinuity lines of unit-length, divergence-free 2D vector fields. The motivation comes from thin-film micromagnetics where these functionals correspond to mesoscopic wall-energies. A natural issue consists in characterizing the line-energy densities for which the functionals are lower semicontinuous for a relevant topology. In fact, this is a necessary condition for being the Γ-limit of a family of energies. A key point in our study is the use of the notion of entropy production borrowed from the field of conservation laws. With this tool, we build a large class of lower semicontinuous line-energies. In particular, we prove that certain power functions lead to such line-energy functionals as conjectured in Ambrosio et al. (Calc Var Partial Differ Equ 9(4):327–355, 1999). We also deduce compactness properties for these functionals leading to the existence of minimizers for their lower semicontinuous envelopes. Another natural question is whether the viscosity solution is a minimizing configuration. We show that the answer is in general negative by exhibiting some special nonconvex domains as counterexamples. However, we establish positive results for some special domains (stadium, ellipse and union of two discs). The case of general convex domains is still open.
Ending Page 418
Page Count 44
Starting Page 375
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 44
Language English
Publisher Springer-Verlag
Publisher Date 2011-07-08
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Methods involving semicontinuity and convergence; relaxation Variational problems in a geometric measure-theoretic setting Variational methods Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Theoretical, Mathematical and Computational Physics Analysis Harmonic maps etc. Magnetic materials Viscosity solutions
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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