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Estimates in the Generalized Morrey Space for Linear Parabolic Systems

by McBride, Matthew Scott

Abstract (Summary)
The purpose of the this paper is to study the parabolic system u_t^{i} - D_&alpha(a_ij^{&alpha&beta}D_&betau^j) = -div f^i in the generalized Morrey Space L_&phi^{2,&lambda} . We would like to understand the regularity of the solutions of this system. It will be shown that 1: if a_ij^{&alpha&beta} in C(Q_T) then Du in L_&phi^{2,&lambda}, and 2: if a_ij^{&alpha&beta} in VMO(Q_T) then Du in L_&phi^{2,&lambda}. Moreover we will be able to obtain estimates on the gradient of the solutions to the system, which will tell us about the regularity of the solutions.
Bibliographical Information:

Advisor:

School:Wright State University

School Location:USA - Ohio

Source Type:Master's Thesis

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ISBN:

Date of Publication:01/01/2007

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