<em>L</em><sup>2,μ</sup>(<em>Q</em>)-estimates for Parabolic Equations and Applications

<em>L</em><sup>2,μ</sup>(<em>Q</em>)-estimates for Parabolic Equations and Applications

Year:    1997

Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 31–44

Abstract

In this paper we derive a priori estimates in the Campanato space L^{2,\mu}(Q_T) for solutions of tbe following parabolic equation u_t - \frac{∂}{∂x_i}(a_{ij}(x,t)u_x_j+a_iu) + b_iu_x_i + cu = \frac{∂}{∂_x_i}f_i + f_0 where {a_{ij}(x, t)} are assumed to be measurable and satisfy the ellipticity condition. The proof is based on accurate DeGiorgi-Nash-Moser's estimate and a modified Poincare's inequality. These estimates are very useful in the study of the regularity of solutions for some nonlinear problems. As a concrete example, we obtain the classical solvability for a strongly coupled parabolic system arising from the thermistor problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1997-JPDE-5580

Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 1 : pp. 31–44

Published online:    1997-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Parabolic equation