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A trace preserving operator and applications. (English) Zbl 1466.35062

Summary: We construct a trace preserving operator which improves the integrability of functions in Sobolev classes refining the ones available in literature. As applications, we prove a \(C^{1,\alpha}\) partial regularity result for local minimizers of quasiconvex integral functionals satisfying non standard \((p, q)\) growth conditions in the borderline case \(p=n-1\) and \(q=n\), and a global integrability result for weak solutions to a nonlinear elliptic system.

MSC:

35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35J50 Variational methods for elliptic systems
35J60 Nonlinear elliptic equations
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