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Kernel estimates for nonautonomous Kolmogorov equations. (English) Zbl 1331.35153
The authors prove kernel estimates for transition probabilities associated with nonautonomous evolution equations. They study global regularity properties and pointwise bounds of the density $$\rho$$. First they establish global boundedness and Sobolev regularity of $$\rho$$ in the case of bounded diffusion coefficients. Then, they use time-dependent Lyapunov functions and an approximation argument based on De Giorgi’s technique to prove global boundedness and pointwise estimates of $$\rho$$ in the general case, where the diffusion coefficients are not assumed to be bounded.

##### MSC:
 35K10 Second-order parabolic equations 35K08 Heat kernel 37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 37L40 Invariant measures for infinite-dimensional dissipative dynamical systems 60J60 Diffusion processes
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