A GRADIENT ESTIMATE FOR SOLUTIONS TO PARABOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

作者：Fan, Jishan^*; Kim, Kyoungsun; Nagayasu, Sei; Nakamura, Gen

来源：Electronic Journal of Differential Equations, 2013, 93.

• Parabolic equations
• discontinuous coefficients
• gradient estimate

Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1,which we called them manifolds of discontinuities. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. Both gradient estimates are independent of the distances between manifolds of discontinuities.

• 出版日期2013-4-11
• 单位南京林业大学