On parabolic equations in one space dimension

2015/05/10 by Н. В. Крылов, Krylov, N. V. · 1 citation
Mathematics · #35K10 #35K15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1505.02330

openalex publication_date 2015/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• On nondivergence form linear parabolic and elliptic equations with degenerate coefficients

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