Abstract
The authors investigate differentiability of the solutions of nonlinear parabolic systems of order 2 m in divergence form of the following type The achieved results are inspired by the paper of Marino and Maugeri 2008, and the methods there applied. This note can be viewed as a continuation of the study of regularity properties for solutions of systems started in Ragusa 2002, continued in Ragusa 2003 and Floridia and Ragusa 2012 and also as a generalization of the paper by Capanato and Cannarsa 1981, where regularity properties of the solutions of nonlinear elliptic systems with quadratic growth are reached. Mathematics Subject Classification (2000) Primary 35K41, 35K55. Secondary 35B65, 35B45, 35D10
Highlights
The study of regularity for solutions of partial differential equations and systems has received considerable attention over the last thirty years
Little is known concerning parabolic systems in divergence form of order 2m with quadratic growth and the corresponding analytic properties of solutions
This note is a natural continuation of the study, carried out in the last decade and a half, of embedding results of Gagliardo-Nirenberg type from which we deduce local differentiability theorems, making use of interpolation theory in Besov spaces
Summary
The study of regularity for solutions of partial differential equations and systems has received considerable attention over the last thirty years. We mention at first the note [8] where the author proves that, let Ω ⊂ Rn an open set, 0 < T
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