Universal singular sets for one-dimensional variational problems

DOI10.1007/BF01206961zbMath0896.49022MaRDI QIDQ1311346

John M. Ball, Nikolai S. Nadirashvili

Publication date: 18 June 1998

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

zbMATH Keywords

multiple integralsLagrange problemregularity properties of minimizersuniversal singular sets

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Existence theories for free problems in one independent variable (49J05)

Related Items (12)

Generic well-posedness of variational problems without convexity assumptions ⋮ TWO POROSITY RESULTS IN MONOTONIC ANALYSIS ⋮ Examples of classically unsolvable scalar regular variational problems satisfying standard growth conditions ⋮ Lebesgue measure of the universal singular set for the simplest problems in the calculus of variations ⋮ Universal singular sets and unrectifiability ⋮ Regularity theory for one-dimensional variational problems with singular ellipticity ⋮ Density of the set of local minimizers for a generic cost function ⋮ Another theorem of classical solvability `in small' for one-dimensional variational problems ⋮ Universal singular sets in the calculus of variations ⋮ The set of divergent infinite products in a Banach space is \(\sigma\)-porous ⋮ Almost all normal sets are strictly normal ⋮ Well-posedness and porosity in the calculus of variations without convexity assumptions

Cites Work

• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• Singular minimisers in the calculus of variations in one dimension
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