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arXiv · 1505.02330

On parabolic equations in one space dimension

N. V. Krylov
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Abstract

Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of $(t,x)$ bounded away from zero. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations.

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N. V. Krylov. 2015-05-10. On parabolic equations in one space dimension. https://arxiv.org/abs/1505.02330

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