FRANK DUZAAR

Optimal regularity for second order parabolic systems via A-caloric approximation

Pages 91-113
Received: 25 January 2005   
Mathematics Subject Classification (2000): 35K55 - 35D10

Abstract: We discuss a new approach to the regularity theory for solutions of second order non-linear parabolic systems. This method is direct, exhibiting the dependence of the regularity estimates on structural data of the coefficients of the parabolic system in explicit form; it requires only weak growth and smoothness assumptions on the coefficients, and it leads to new regularity results which give the best possible modulus of continuity for the spatial derivative of the solution. The present note is a summary of parts of the results obtained in [16].