L (Q)-Estimates for Parabolic Equations and Applications
نویسنده
چکیده
In this paper we derive L (QT )-estimates for the rst order derivatives of solutions to the following parabolic equation ut @ @xi (aij(x; t)uxj + aiu) + biuxi + cu = @ @xi fi + f0; where faij(x; t)g are assumed to be measurable and satis ed the ellipticity condition. The main idea is based on De Giorgi-Nash's estimates and Moser's iteration technique. These estimates are very useful in 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. AMS(MOS) Subject Classi cation: 35K20, 35K55.
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