TY - JOUR
T1 - <em>L</em><sup>2,μ</sup>(<em>Q</em>)-estimates for Parabolic Equations and Applications
AU - Hongming Yin 
JO - Journal of Partial Differential Equations
VL - 1
SP - 31
EP - 44
PY - 1997
DA - 1997/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5580.html
KW - Parabolic equation
KW - a priori estimates in Campanato space
KW - DeGiorgi-Nash-Moser's estimate
KW - a modified Poincare's inequality
AB -  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.