Analogs of Giraud's theorem for a second-order parabolic equation

DOI10.1007/BF00967266zbMath0265.35041MaRDI QIDQ2562301

L. I. Kamynin, B. N. Khimchenko

Publication date: 1973

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order parabolic equations (35K10)

Related Items (16)

Unilateral estimates for solutions to the second and third boundary value problems (with oblique derivative) for a strongly dissipative second-order parabolic equation ⋮ Uniqueness of solutions of initial-boundary value problems for parabolic systems with dini-continuous coefficients in domains on the plane ⋮ Existence and uniqueness of the solution to a degenerate third boundary value problem for a multidimensional parabolic equation ⋮ Local behavior of the solution of a second-order parabolic equation near the lower section of a parabolic boundary ⋮ A parabolic analogue of the higher-order comparison theorem of De Silva and Savin ⋮ Poisson potential in the first initial-boundary value problem for a parabolic system in a semibounded domain on the plane ⋮ On the unique solvability of initial-boundary value problems for parabolic systems in bounded plane domains with nonsmooth lateral boundaries ⋮ Theorem on the oblique derivative for uniformly parabolic equations of the second order ⋮ Uniqueness of solutions of the first and second initial-boundary value problems for parabolic systems in bounded domains on the plane ⋮ Uniqueness of solutions to initial boundary value problems for parabolic systems in plane bounded domains with nonsmooth lateral boundaries ⋮ The maximum principle and local Lipschitz estimates near the laterial boundary for solutions of second-order parabolic equations ⋮ Hamiltonian formulation and fundamental conservation laws for a model of small elliptical vortices ⋮ Uniqueness of the solution of the first initial-boundary value problem for a parabolic system with differentiable coefficients in a half-strip with nonsmooth lateral boundary ⋮ The principle of the maximum and boundary Lipschitz bounds for the solution of a second order elliptic-parabolic equation ⋮ A linear boundary value problem for a second-order elliptic-parabolic equation ⋮ Investigations on an anisotropic strict extremum principle for elliptic- parabolic equations of second order

Cites Work

• Remarks on the maximum principle for parabolic equations and its applications
• A Remark on Linear Elliptic Differential Equations of Second Order
• A strong maximum principle for parabolic equations
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