# zbMATH — the first resource for mathematics

On weak minima of certain integral functionals. (English) Zbl 0920.49021
The paper deals with the regularity of the weak minima of some integral functionals not necessarily differentiable. By assuming a polynomial growth and a Lipschitz type condition on the integrand, the author proves that a weak minimum $$u\in W^{1,r}_{\text{loc}}$$, $$r< p$$ ($$p$$ is related to the growth of the integrand), is indeed in the space $$W^{1,p}_{\text{loc}}$$, if $$r$$ is close enough to $$p$$. The main arguments in the proof are the Hodge decomposition and some reverse Hölder inequalities.
Reviewer: R.Schianchi (Roma)

##### MSC:
 49N60 Regularity of solutions in optimal control 49J45 Methods involving semicontinuity and convergence; relaxation 42B25 Maximal functions, Littlewood-Paley theory
Full Text: