Methods and Applications of Analysis

Volume 20 (2013)

Number 1

Schauder estimates for solutions of higher-order parabolic systems

Pages: 47 – 68

DOI: http://dx.doi.org/10.4310/MAA.2013.v20.n1.a3

Author

Serena Boccia (Dipartimento di Matematica, Università di Salerno, Fisciano (SA), Italy)

Abstract

We prove global Schauder estimates for the derivatives of solutions to non-divergence form higher-order parabolic systems. All coefficients are taken only measurable in the time variable and Hölder continuous in the space variables. Moreover we require that the principal coefficients satisfy the so-called Legendre-Hadamard ellipticity condition. Using such estimates and some classical results, we also give a proof of existence and uniqueness for the Cauchy problem.

Keywords

parabolic systems, Schauder estimates, Hölder norms

2010 Mathematics Subject Classification

35B45, 35K41

Full Text (PDF format)