@Article{JPDE-10-31,
author = {Hongming Yin },
title = {<em>L</em><sup>2,μ</sup>(<em>Q</em>)-estimates for Parabolic Equations and Applications},
journal = {Journal of Partial Differential Equations},
year = {1997},
volume = {10},
number = {1},
pages = {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&#39;s estimate and a modified Poincare&#39;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.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5580.html}
}