The first boundary value problem for nondivergent second order parabolic equations with discontinuous coefficients. (English. Russian original) Zbl 0663.35033

Alkhutov, Yu. A.; Mamedov, I. T.

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 \[ Lu=\sum^{n}_{i,k=1}a_{ik}(t,x)u_{x_ ix_ k}-u_ t=f(t,x). \]

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