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L’auteur prouve deux théorèmes d’unicité locale du problème de Cauchy pour des opérateurs linéaires de symboles principaux $p$ réels. Il se place dans le cas où $p$ possède des points critiques réels ( $p = d p = 0$ ), au voisinage desquels il suppose une condition faible de “pseudo-convexité” (au sens d’Hörmander). Il donne alors des conditions sur le symbole sous-principal de l’opérateur qui assurent l’unicité.

Uniqueness for first-order hyperbolic systems - with applications to secnd-order elliptic third-order and Maxwell's equations.

Reinhard Racke (1987)

Journal für die reine und angewandte Mathematik

Un'osservazione sulla risolubilità formale delle equazioni alle derivate parziali lineari a coefficienti costanti

Giuliano Bratti (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

L'autore dà una condizione necessaria e sufficiente per la risolubilità formale degli operatori differenziali a coefficienti costanti, lineari, $p (D)$ , in termini di prolungamento, come distribuzioni, delle $u \in D^{'} (R^{n} - \{0\})$ , tali che $p (- D) u = 0$ .

Various representations for the system of hyperbolic equations with singular coefficients.

Nasim, Adib Adel (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

Weakly semibounded boundary problems and sesquilinear forms

Gerd Grubb (1973)

Annales de l'institut Fourier

Let $A$ be a $2 m$ order differential operator in a hermitian vector bundle $E$ over a compact riemannian manifold $\overline{Ω}$ with boundary $Γ$ ; and denote by $A_{B}$ the realization defined by a normal differential boundary condition $B ρ u = 0$ ( $u \in H^{2 m} (E)$ , $ρ u =$ Cauchy data). We characterize, by an explicit condition on $A$ and $B$ near $Γ$ , the realizations $A_{B}$ for which there exists an integro-differential sesquilinear form $a_{B} (u, ν)$ on $H^{m} (E)$ such that $(A u, ν) = a_{B} (u, ν)$ on $D (A_{B})$ ; moreover we show that these are exactly the realizations satisfying a weak semiboundedness estimate:...

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The general method for solving of the boundary problems for the partial differential equations of any order II

The general method for solving the partial differential equation of any order with unknown function depending on any number of arguments and the system of such equations

The Laplace method of the linear partial differential equations of the $n$ -th order

Théorème de Cauchy-Kovalevsky et théorème d'unicité d'Holmgren pour des fonctions analytiques d'une infinité de variables

Time deformations of powers of the wave operator.

Über lineare partielle Differentialgleichungen zweiter Ordnung mit Bergman-Operatoren der Klasse P.

Über lineare partielle Differentialgleichungen zweiter Ordnung mit Fundamentalsystemen.

Un teorema sui polinomi differenziali omogenei in $R^{2}$

Unicité du problème de Cauchy pour des opérateurs du second ordre à symboles réels

Uniqueness for first-order hyperbolic systems - with applications to secnd-order elliptic third-order and Maxwell's equations.

Un'osservazione sulla risolubilità formale delle equazioni alle derivate parziali lineari a coefficienti costanti

Various representations for the system of hyperbolic equations with singular coefficients.

Weakly semibounded boundary problems and sesquilinear forms

Zur Existenz und Charakterisierung von Bergman-Operatoren. I. Der eingliedrige Lösungsansatz.

Асимптотические решения уравнений с комплексными характеристиками

Конечнозонные решения на языке автоморфных функций. Уравнение Кадомцева-Петвиашвили

Локальные анизотропные гёльдеровы оценки решений уравнения квазиэллиптического типа.

Мультипликаторные операторы, связанные с задачей Коши для волнового уравнения. Разностная регуляризация

Некоторые вопросы теории двумерных дифференциальных уравнений и систем 2-го порядка

Некоторые теоремы об особенностях решений дифференциальных уравнений со взвешенными главными символами

Currently displaying 81 – 100 of 119