Remarks on the regularity of the minimizers of certain degenerate functionals. (English) Zbl 0607.49003

The authors study the partial or global regularity of the minimizers for integrals functionals of the type \(\int_{\Omega}f(x,u,Du)dx\) where \(\Omega\) is a bounded open set in \({\mathbb{R}}^ n\), \(u: \Omega\to {\mathbb{R}}^ N\) and f is subjected to a growth condition in the last variable, which is polynomial like \(| p|^ m\), \(m\geq 2\). The treatment is very careful and articulate and includes also many hard cases as, for example, that of degenerate integrands. The theorems they obtain extend and improve various well-known results on the subject (see the references).
Reviewer: A.Salvadori


49J10 Existence theories for free problems in two or more independent variables
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35D10 Regularity of generalized solutions of PDE (MSC2000)
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