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

DOI10.1186/s13661-018-1047-2zbMath1499.74021OpenAlexW2888196895MaRDI QIDQ2126444

Ali Taheri, George Morrison

Publication date: 19 April 2022

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-018-1047-2

zbMATH Keywords

nonlinear elasticitynonlinear elliptic systemsgeodesics on \(\mathrm{SO}(n)\)incompressible twistscurl-free vector fieldsmultiple stationary loopsweighted Dirichlet-type Lagrangians

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Nonlinear elliptic equations (35J60) Regularity of solutions in optimal control (49N60) Methods involving semicontinuity and convergence; relaxation (49J45) Boundary value problems for second-order elliptic systems (35J57)

Cites Work

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• Singular limit solutions for a 2-dimensional semilinear elliptic system of Liouville type
• Spherical twists, stationary paths and harmonic maps from generalised annuli into spheres
• Sufficient conditions for regularity of area-preserving deformations
• Twist maps as energy minimisers in homotopy classes: symmetrisation and the coarea formula
• Local minimizers and quasiconvexity -- the impact of topology
• On double-covering stationary points of a constrained Dirichlet energy
• Homotopy classes of self-maps of annuli, generalised twists and spin degree
• Generalised twists, stationary loops, and the Dirichlet energy over a space of measure preserving maps
• Minimizing the Dirichlet energy over a space of measure preserving maps
• Convexity conditions and existence theorems in nonlinear elasticity
• Whirl mappings on generalised annuli and the incompressible symmetric equilibria of the Dirichlet energy
• Geodesics on \(\mathrm{SO}(n)\) and a class of spherically symmetric maps as solutions to a nonlinear generalised harmonic map problem
• Annular rearrangements, incompressible axi-symmetric whirls and \(L^1\)-local minimisers of the distortion energy
• On the well-posedness of global fully nonlinear first order elliptic systems
• 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 the partial regularity of energy-minimizing, area-preserving maps
• On the uniqueness of energy minimizers in finite elasticity
• Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain
• Some Open Problems in Elasticity
• Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions
• 𝑛-Harmonic Mappings Between Annuli: The Art of Integrating Free Lagrangians
• Function Spaces and Partial Differential Equations
• Extremal mappings of finite distortion

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