Alkhutov, Yu. A.; Mamedov, I. T. The first boundary value problem for nondivergent second order parabolic equations with discontinuous coefficients. (English. Russian original) Zbl 0663.35033 Math. USSR, Sb. 59, No. 2, 471-495 (1988); translation from Mat. Sb., Nov. Ser. 131(173), No. 4(12), 471-495 (1986). This paper is concerned with the questions of solvability and smoothness of weak solutions of the first boundary value problem for a parabolic equation of the form \[ Lu=\sum^{n}_{i,k=1}a_{ik}(t,x)u_{x_ ix_ k}-u_ t=f(t,x). \] Cited in 4 ReviewsCited in 12 Documents MSC: 35K20 Initial-boundary value problems for second-order parabolic equations 35B65 Smoothness and regularity of solutions to PDEs 35R05 PDEs with low regular coefficients and/or low regular data 35D05 Existence of generalized solutions of PDE (MSC2000) Keywords:solvability; smoothness; weak solutions; first boundary value problem PDF BibTeX XML Cite \textit{Yu. A. Alkhutov} and \textit{I. T. Mamedov}, Math. USSR, Sb. 59, No. 2, 471--495 (1988; Zbl 0663.35033); translation from Mat. Sb., Nov. Ser. 131(173), No. 4(12), 471--495 (1986) Full Text: DOI OpenURL