𝑛-Harmonic Mappings Between Annuli: The Art of Integrating Free Lagrangians
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Publication:5403720
DOI10.1090/S0065-9266-2011-00640-4zbMath1294.30042arXiv1102.0959MaRDI QIDQ5403720
Publication date: 18 March 2014
Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1102.0959
Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Variational methods for second-order elliptic equations (35J20) Extremal problems for conformal and quasiconformal mappings, other methods (30C75)
Related Items (47)
On a class of stationary loops on \(\mathbf{SO}(n)\) and the existence of multiple twisting solutions to a nonlinear elliptic system subject to a hard incompressibility constraint ⋮ Whirl mappings on generalised annuli and the incompressible symmetric equilibria of the Dirichlet energy ⋮ \(\sigma _2\)-diffeomorphisms between 4-dimensional annuli ⋮ On multiple solutions to a family of nonlinear elliptic systems in divergence form coupled with an incompressibility constraint ⋮ Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids ⋮ The Dirichlet principle for inner variations ⋮ Topology of twists, extremising twist paths and multiple solutions to the nonlinear system in variation \(\mathscr{L}[u = \nabla \mathscr{P}\)] ⋮ Total energy of radial mappings ⋮ Mappings of least Dirichlet energy and their Hopf differentials ⋮ The Sobolev Jordan-Schönflies problem ⋮ Nitsche type inequality for hyperbolic harmonic mappings between annuli in the unit ball \(\mathbb{B}^3\) ⋮ Jacobian of weak limits of Sobolev homeomorphisms ⋮ The existence of multiple topologically distinct solutions to \(\sigma_{2, p}\)-energy ⋮ Annular rearrangements, incompressible axi-symmetric whirls and \(L^1\)-local minimisers of the distortion energy ⋮ The interplay between two Euler-Lagrange operators relating to the nonlinear elliptic system \(\Sigma [(u, {\mathscr{P}}), \varOmega\)] ⋮ \((n,\rho)\)-harmonic mappings and energy minimal deformations between annuli ⋮ Existence of energy-minimal diffeomorphisms between doubly connected domains ⋮ The Nitsche conjecture ⋮ Spherical twists as the \(\sigma_{2}\) harmonic maps from \(n\)-dimensional annuli into \(\mathbb {S}^{n-1}\) ⋮ On the uniqueness and monotonicity of energy minimisers in the homotopy classes of incompressible mappings and related problems ⋮ Regularity of quasi-\(n\)-harmonic mappings into NPC spaces ⋮ A Neohookean Model of Plates ⋮ Dirichlet-type energy of mappings between two concentric annuli ⋮ Deformations of bi-conformal energy and a new characterization of quasiconformality ⋮ Twist maps as energy minimisers in homotopy classes: symmetrisation and the coarea formula ⋮ Limits of Sobolev homeomorphisms ⋮ An infinite scale of incompressible twisting solutions to the nonlinear elliptic system \(\mathcal{L} [u; \mathsf{A}, \mathsf{B} = \nabla \mathcal{P}\) and the discriminant \(\varDelta(h, g)\)] ⋮ On J. C. C. Nitsche type inequality for annuli on Riemann surfaces ⋮ Doubly connected minimal surfaces and extremal harmonic mappings ⋮ Smoothing Defected Welds and Hairline Cracks ⋮ Invertibility versus Lagrange equation for traction free energy-minimal deformations ⋮ Neohookean deformations of annuli, existence, uniqueness and radial symmetry ⋮ Radial symmetry of \(p\)-harmonic minimizers ⋮ Neohookean deformations of annuli in the higher dimensional Euclidean space ⋮ Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity ⋮ Monotone Sobolev mappings of planar domains and surfaces ⋮ Harmonic maps between two concentric annuli in \(\mathbb{R}^3\) ⋮ Radial symmetry of minimizers to the weighted Dirichlet energy ⋮ Hyperelastic deformations and total combined energy of mappings between annuli ⋮ Energy minimisers with prescribed Jacobian ⋮ Deformations of finite conformal energy: Boundary behavior and limit theorems ⋮ The existence of minimizers of energy for diffeomorphisms between two-dimensional annuli in \(\mathbb{R}^2\) and \(\mathbb{R}^3\) ⋮ Hyperelastic deformations of smallest total energy ⋮ The Nitsche phenomenon for weighted Dirichlet energy ⋮ On the existence and multiplicity of topologically twisting incompressible $H$-harmonic maps and a structural H-condition ⋮ Three-spheres theorem for \(p\)-harmonic mappings ⋮ Energy-minimal Principles in Geometric Function Theory.
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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- Unnamed Item
- Existence of energy-minimal diffeomorphisms between doubly connected domains
- Doubly connected minimal surfaces and extremal harmonic mappings
- Regularity of minima: an invitation to the dark side of the calculus of variations.
- Deformations of annuli with smallest mean distortion
- Null Lagrangians, weak continuity, and variational problems of arbitrary order
- On the existence of harmonic diffeomorphisms between surfaces
- Convexity conditions and existence theorems in nonlinear elasticity
- Regularity for a class of nonlinear elliptic systems
- A uniqueness theorem for surfaces of least area with partially free boundaries on obstacles
- The \(p\)-harmonic approximation and the regularity of \(p\)-harmonic maps
- On the Nitsche conjecture for harmonic mappings in \(\mathbb R^2\) and \(\mathbb R^3\)
- A note on extremal mappings of finite distortion
- The null set of the Euler-Lagrange operator
- A compactness theorem of \(n\)-harmonic maps
- Regularity of the inverse of a planar Sobolev homeomorphism
- On the smoothness of isometries
- Distortion of quasiconformal and quasiregular mappings at extremal points
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Harmonic mappings of an annulus, Nitsche conjecture and its generalizations
- The harmonic mapping problem and affine capacity
- Deformations of finite conformal energy: Boundary behavior and limit theorems
- THE MODULUS OF THE IMAGE ANNULI UNDER UNIVALENT HARMONIC MAPPINGS AND A CONJECTURE OF NITSCHE
- A Variational Method in the Theory of Harmonic Integrals, II
- Analytical foundations of the theory of quasiconformal mappings in R^n
- Homeomorphisms in the Sobolev space W 1,n–1
- Mappings minimizing theLp norm of the gradient
- On the Module of Doubly-Connected Regions Under Harmonic Mappings
- Rings and Quasiconformal Mappings in Space
- On Mappings with Integrable Dilatation
- The Topology of (Path) Surfaces
- The Hopf-Laplace equation: harmonicity and regularity
- The Nitsche conjecture
- Extremal mappings of finite distortion
- Deformations of finite conformal energy: existence and removability of singularities
- Mappings of finite distortion: Monotonicity and continuity
- Univalent harmonic mappings of annuli and a conjecture of J. C. C. Nitsche
- Behaviour of doubly connected minimal surfaces at the edges of the support surfaces
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