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Regularity under general and \(p,q\)-growth conditions. (English) Zbl 1439.35102

Summary: This paper deals with existence and regularity in variational problems related to partial differential equations and systems – both in the elliptic and in the parabolic contexts – and to calculus of variations, under general and \( p,q\)-growth conditions. The manuscript is dedicated to my friend and colleague Patrizia Pucci, with great esteem and sympathy.

MSC:

35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35J47 Second-order elliptic systems
35J60 Nonlinear elliptic equations
35K40 Second-order parabolic systems
35K55 Nonlinear parabolic equations
49J40 Variational inequalities
49N60 Regularity of solutions in optimal control
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