Qualitative theory of second order linear partial differential equations. (Russian) Zbl 0656.35012

Topic of the article is the qualitative theory of second order elliptic and parabolic equations. The behaviour of solutions in infinite domains, in a neighbourhood of the boundary of the domain is investigated. The question of influence of the smoothness of coefficients on the properties of solutions is considered. Questions of uniqueness and correctness of the Cauchy problem are discussed.


35B40 Asymptotic behavior of solutions to PDEs
35K10 Second-order parabolic equations
35J15 Second-order elliptic equations
35K15 Initial value problems for second-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs