The aim of this paper is to introduce the new notion of quasi-minima (Q-minima) of regular functionals in the calculus of variations. The interest of this notion lies mainly in its unifying features; it includes among other things minima of variational integrals, solutions of elliptic partial differential equations and systems, quasi-regular mappings. We prove some regularity results for Q-minima in L^p and C^0,alpha-spaces as well as qualitative features: Liouville property, weak maximum principle, removal of singularities.
Quasi-minima
GIAQUINTA, Mariano;
1984
Abstract
The aim of this paper is to introduce the new notion of quasi-minima (Q-minima) of regular functionals in the calculus of variations. The interest of this notion lies mainly in its unifying features; it includes among other things minima of variational integrals, solutions of elliptic partial differential equations and systems, quasi-regular mappings. We prove some regularity results for Q-minima in L^p and C^0,alpha-spaces as well as qualitative features: Liouville property, weak maximum principle, removal of singularities.File in questo prodotto:
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