Quasiconvexity and relaxation of nonconvex problems in the calculus of variations

DOI10.1016/0022-1236(82)90046-5zbMath0547.49003OpenAlexW2014133061MaRDI QIDQ798943

Publication date: 1982

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(82)90046-5

zbMATH Keywords

quasiconvexity relaxation

Mathematics Subject Classification ID

Nonlinear programming (90C30) Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45) Convexity of real functions of several variables, generalizations (26B25) Numerical methods of relaxation type (49M20)

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Cites Work