Regularity under general and $ p,q- $ growth conditions

Paolo Marcellini

doi:10.3934/dcdss.2020155

Article Contents

2020, Volume 13, Issue 7: 2009-2031. Doi: 10.3934/dcdss.2020155

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–fractional equations without the Ambrosetti–Rabinowitz condition Next Article On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions

Regularity under general and $ p,q- $ growth conditions

Paolo Marcellini

Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 - Firenze, Italy

Received: July 2018

Revised: July 2018

Published: April 2020

The author is a member of GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica)

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Abstract

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.

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Mathematics Subject Classification: 35B45, 35B65, 35J60, 35K10, 35K55, 49J40, 49N60.

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