The Carleman formula for the Helmholtz equation on the plane.
The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable
We discuss the local existence and uniqueness of solutions of certain nonstrictly hyperbolic systems, with Hölder continuous coefficients with respect to time variable. We reduce the nonstrictly hyperbolic systems to the parabolic ones and by use of the Tanabe-Sobolevski’s method and the Banach scale method we construct a semi-group which gives a representation of the solution to the Cauchy problem.
The complex reflection method for some classes of equations with the third derivative distinguished.
The fundamental solution for a consistent complex model of the shallow shell equations.
The fundamental solution of a modified Oseen problem.
The logarithmic gradient of the kernel of the heat equation with drift on a Riemannian manifold.
The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation
Let L be a second order, linear, parabolic partial differential operator, with bounded Hölder continuous coefficients, defined on the closure of the strip . We prove a representation theorem for an arbitrary function, in terms of the fundamental solution of the equation Lu=0. Such a theorem was proved in an earlier paper for a parabolic operator in divergence form with coefficients, but here much weaker conditions suffice. Some consequences of the representation theorem, for the solutions of...
The Riccati differential equation and a diffusion-type equation.
The spread of the potential on a weighted graph.
Time deformations of powers of the wave operator.
Über eine nichtlineare partielle Diferentialgleleichung II ordnung in der nichtanalytische funktionen Erssheinen
Über lineare partielle Differentialgleichungen zweiter Ordnung mit Fundamentalsystemen.
Un’applicazione del teorema del grafico chiuso alla risolubilità di sistemi differenziali del tipo :
Zentrale Distributionen auf Exponentialgruppen.
Асимптотика решений некоторых эллиптических уравнений в неограниченных областях
Асимптотика фундаментального решения параболического уравнения при t
Асимптотики фундаментальных решений дивергентных дифференциальных уравнений второго порядка
Исправления к статье "О фундаментальных решениях параболических систем. II"
Матричные ряды Лауричеллы и краевые задачи для вырождающихся эллиптических систем.
Метод Ж. Адамара для некоторых классов гиперболических уравнений с переменными коэффициентами