Existence and partial regularity in the calculus of variations

DOI10.1007/BF01773940zbMath0648.49008OpenAlexW2067644059MaRDI QIDQ1105189

Min-Chun Hong

Publication date: 1987

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01773940

zbMATH Keywords

partial regularityquasiconvex functionalsgeneralized quasi-minima

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20) Convexity of real functions of several variables, generalizations (26B25)

Related Items

\(C^{1,\alpha}\) convergence of a Ginzburg-Landau type minimizer in higher dimensions, Partial regularity of multiple variational integrals of any order, Unnamed Item, A regularity theorem for minimisers of quasiconvex integrals: the case 1 <p<2, Regularity of minima: an invitation to the dark side of the calculus of variations., Partial regularities of minimizers of certain quadratic functionals with unbounded obstacles, Limiting properties of the second order Ginzburg-Landau minimizers, Optimal partial regularity of minimizers of quasiconvex variational integrals, Partial regularity for minimizers of variational integrals with discontinuous integrands, Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations

Cites Work

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• On the regularity of the minima of variational integrals
• Convexity conditions and existence theorems in nonlinear elasticity
• Nonlinear elliptic systems with quadratic growth
• A transmission problem in the calculus of variations
• Quasi-convessita e semicontinuita per integrali multipli di ordine superiore
• Quasi-convexity and the lower semicontinuity of multiple integrals
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Nonconvex minimization problems
• Strict convexity, strong ellipticity, and regularity in the calculus of variations
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