Partial regularity for biharmonic maps, revisited

DOI10.1007/s00526-008-0175-4zbMath1151.58011OpenAlexW1997779676MaRDI QIDQ933772

Michael Struwe

Publication date: 25 July 2008

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/3958

zbMATH Keywords

partial regularitygauge theoryMorrey spacebiharmonic maps

Mathematics Subject Classification ID

Related Items (31)

Neck analysis for biharmonic maps ⋮ Partial regularity of polyharmonic maps to targets of sufficiently simple topology ⋮ Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane-Emden equation ⋮ Quantitative stratification and higher regularity for biharmonic maps ⋮ Uniqueness of tangent cones for biharmonic maps with isolated singularities ⋮ Bubbling phenomena of biharmonic maps ⋮ Heat flow of extrinsic biharmonic maps from a four dimensional manifold with boundary ⋮ Doubling annulus Pohožaev type identity and applications to approximate biharmonic maps ⋮ Sharp Morrey regularity theory for a fourth order geometrical equation ⋮ Existence of extrinsic polyharmonic maps in critical dimensions ⋮ Bubbling analysis for extrinsic biharmonic maps from general Riemannian 4-manifolds ⋮ Blow-up analysis and boundary regularity for variationally biharmonic maps ⋮ Energy identity of approximate biharmonic maps to Riemannian manifolds and its application ⋮ Boundary partial regularity for a class of biharmonic maps ⋮ Partial regularity of a minimizer of the relaxed energy for biharmonic maps ⋮ Regularity of solutions for a fourth‐order elliptic system via Conservation law ⋮ The Lamm-Rivière system. I: \(L^p\) regularity theory ⋮ Well-posedness for the heat flow of biharmonic maps with rough initial data ⋮ Uhlenbeck's decomposition in Sobolev and Morrey-Sobolev spaces ⋮ Regularity and uniqueness of a class of biharmonic map heat flows ⋮ Boundary regularity for minimizing biharmonic maps ⋮ \(\varepsilon\)-regularity for systems involving non-local, antisymmetric operators ⋮ Conservation laws for even order elliptic systems in the critical dimension -- a new approach ⋮ An optimal partial regularity result for minimizers of an intrinsically defined second-order functional ⋮ On minimizing extrinsic biharmonic maps ⋮ Higher order intrinsic weak differentiability and Sobolev spaces between manifolds ⋮ A regularity result for polyharmonic maps with higher integrability ⋮ An 𝐿^{𝑝} regularity theory for harmonic maps ⋮ Continuity of almost harmonic maps with the perturbation term in a critical space ⋮ Regularity of weak solutions to higher order elliptic systems in critical dimensions ⋮ \(L^p\)-regularity for fourth order elliptic systems with antisymmetric potentials in higher dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• A monotonicity formula for stationary biharmonic maps
• Connections with \(L^ p \)bounds on curvature
• A partial regularity result for a class of stationary Yang-Mills fields in high dimension.
• On biharmonic maps and their generalizations
• Conservation laws for conformally invariant variational problems
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Composition Operators on Potential Spaces
• Stationary biharmonic maps fromRm into a Riemannian manifold
• A singularity removal theorem for Yang-Mills fields in higher dimensions
• GAGLIARDO–NIRENBERG INEQUALITIES WITH A BMO TERM
• Partial regularity for harmonic maps and related problems

This page was built for publication: Partial regularity for biharmonic maps, revisited