On a parabolic equation with a singular lower order term

Zhang, Qi

doi:10.1090/S0002-9947-96-01675-3

On a parabolic equation with a singular lower order term
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by Qi Zhang

Trans. Amer. Math. Soc. 348 (1996), 2811-2844

DOI: https://doi.org/10.1090/S0002-9947-96-01675-3

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Abstract:

We obtain the existence of the weak Green’s functions of parabolic equations with lower order coefficients in the so called parabolic Kato class which is being proposed as a natural generalization of the Kato class in the study of elliptic equations. As a consequence we are able to prove the existence of solutions of some initial boundary value problems. Moreover, based on a lower and an upper bound of the Green’s function, we prove a Harnack inequality for the non-negative weak solutions.

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