On A parabolic equation with a singular lower order term |
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Authors: | Qi Zhang |
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Institution: | Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 |
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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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