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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 51
  3. Calculus of Variations and Partial Differential Equations : Volume 51, Issue 3-4, November 2014
  4. Intrinsically $$p$$ -biharmonic maps
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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 51, Issue 3-4, November 2014
Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces
Regularity of minimal hypersurfaces with a common free boundary
Continuous dependence estimates for the ergodic problem of Bellman equation with an application to the rate of convergence for the homogenization problem
Global Calderón–Zygmund theory for nonlinear parabolic systems
Intrinsically $$p$$ -biharmonic maps
Existence of solutions to the Kobayashi–Warren–Carter system
A quantitative estimate for mappings of bounded inner distortion
Derivation of a homogenized nonlinear plate theory from 3d elasticity
Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds
Semiclassical limits of ground state solutions to Schrödinger systems
Infinitely many positive solutions for nonlinear equations with non-symmetric potentials
A sharp strong maximum principle and a sharp unique continuation theorem for singular minimal hypersurfaces
Analyse sur un demi-espace hyperbolique et poly-homogénéité locale
Local gradient estimate for harmonic functions on Finsler manifolds
Biharmonic elliptic problems involving the 2nd Hessian operator
Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities
Global existence of weak solution for the 2-D Ericksen–Leslie system
Partial Sobolev spaces and anisotropic smectic liquid crystals
Calculus of Variations and Partial Differential Equations : Volume 51, Issue 1-2, September 2014
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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Intrinsically $$p$$ -biharmonic maps

Content Provider SpringerLink
Author Moser, Roger Hornung, Peter
Copyright Year 2013
Abstract For a compact Riemannian manifold $$N$$ , a domain $$\Omega \subset \mathbb {R}^m$$ and for $$p\in (1, \infty )$$ , we introduce an intrinsic version $$E_p$$ of the $$p$$ -biharmonic energy functional for maps $$u : \Omega \rightarrow N$$ . This requires finding a definition for the intrinsic Hessian of maps $$u : \Omega \rightarrow N$$ whose first derivatives are merely $$p$$ -integrable. We prove, by means of the direct method, existence of minimizers of $$E_p$$ within the corresponding intrinsic Sobolev space, and we derive a monotonicity formula. Finally, we also consider more general functionals defined in terms of polyconvex functions.
Ending Page 620
Page Count 24
Starting Page 597
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 51
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2013-11-19
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Harmonic maps etc. Variational methods for higher-order elliptic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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