The Dirichlet integral for mappings between manifolds: Cartesian currents and homology

DOI10.1007/BF01934329zbMath0762.49018OpenAlexW2001614106MaRDI QIDQ1195982

Giuseppe Modica, Jiří Souček, Mariano Giaquinta

Publication date: 12 January 1993

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165005

zbMATH Keywords

homologyCartesian currentsvariational problemsDirichlet integral

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20)

Related Items

Further remarks on the lower semicontinuity of polyconvex integrals, Homotopy types for tamely approximable Sobolev maps between manifolds, The relaxed Dirichlet energy of manifold constrained mappings, Some new properties of Sobolev mappings: intersection theoretical approach, Weak and strong density results for the Dirichlet energy, On the minimizers of the relaxed energy functional of mappings from higher dimensional balls into \(S^{2}\), Ground states in complex bodies, Energy estimate, energy gap phenomenon, and relaxed energy for Yang-Mills functional, Variational problems for maps of bounded variation with values in \(S^ 1\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Area-minimizing currents bounded by higher multiples of curves
• Boundary regularity and the Dirichlet problem for harmonic maps
• A new proof of the compactness theorem for integral currents
• Infima of energy functionals in homotopy classes of mappings
• Harmonic maps with defects
• Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity
• The Dirichlet energy of mappings with values into the sphere
• The existence of minimal immersions of 2-spheres
• Variational integrals on mappings of bounded variation and their lower semicontinuity
• The approximation problem for Sobolev maps between two manifolds
• A remark on \(H^ 1\) mappings
• Some extremal questions for simplicial complexes. III: Problems of the geometry and analysis of the higher Euclidean spaces. V: The relative area of a Klein bottle
• Normal and integral currents
• The Least Area Bounded by Multiples of a Curve
• Colloquium lectures on geometric measure theory