Feller Evolution Families and Parabolic Equations with Form-bounded Vector Fields
نویسنده
چکیده
We show that the weak solutions of parabolic equation ∂tu−∆u+ b(t, x) · ∇u = 0 with vector field b(t, x) satisfying form-boundedness condition constitute a Feller evolution family and, thus, determine a strong Markov process. Our proof uses a Moser-type iterative procedure and an a priori estimate on the L-norm of the gradient of solution in terms of the L-norm of the gradient of initial function.
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تاریخ انتشار 2014