Existence and fractional regularity of solutions for a doubly nonlinear differential inclusion

Author(s)

Boldrini, Jose Luiz ^[1] ; de Miranda, Luis H. ^[2] ; Planas, Gabriela ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Matemat, Inst Matemat Estat & Comp Cient, BR-13083859 Campinas, SP - Brazil

^[2] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF - Brazil

• Document type: Journal article
• Source: JOURNAL OF EVOLUTION EQUATIONS; v. 13, n. 3, p. 535-560, SEP 2013.
• Web of Science Citations: 3

Abstract

This article considers the issues of existence and regularity of solutions to the following doubly nonlinear differential inclusion omega(t) + alpha(omega(t)) - Delta omega - Delta(p)omega (sic) f where alpha is a maximal monotone operator in and Delta (p) denotes the p-Laplacian with p > 2. The investigation on fractional regularity is based on the Galerkin method combined with a suitable basis for W (1,p) , which we exhibit as a preliminary result. This approach also allows the obtaining of estimates in the so-called Nikolskii spaces, since it balances the interplay between the maximal monotone operator with the appearing higher order nonlinear terms. (AU)

• FAPESP's process: 08/09342-3 - Mathematical analysis for phase-field models
• Grantee: Gabriela Del Valle Planas
• Support Opportunities: Regular Research Grants