Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Interpolation inequalities for weak solutions of nonlinear parabolic systems | Floridia and Ragusa Journal of Inequalities and Applications 2011 2011 42 http content 2011 1 42 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Interpolation inequalities for weak solutions of nonlinear parabolic systems Giuseppe Floridia and Maria Alessandra Ragusa Correspondence maragusa@dmi. Dipartimento di Matematica e Informatica Universitá di Catania Viale A. Doria 6 95125 Catania Italy Springer Abstract The authors investigate differentiability of the solutions of nonlinear parabolic systems of order 2 m in divergence form of the following type -1 WD aa X Du d- 0. a m 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 Keywords Higher order nonlinear parabolic systems Divergence form Interpolation theory Besov spaces Local differentiability 1 Introduction The study of regularity for solutions of partial differential equations and systems has received considerable attention over the last thirty years. On the other hand little is known concerning parabolic systems in divergence form of order 2m with quadratic growth and the corresponding analytic properties of solutions. To such classes of systems our attention is devoted. 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 see .
