Showing papers in "Communications in Partial Differential Equations in 1984"
TL;DR: On considere l'operateur de Schrodinger a potentiel a puits multiples, on etudie le comportement des valeurs propres qui tendent vers un niveau d'energie donne E 0 ∈R quand h→0
Abstract: On considere l'operateur de Schrodinger a potentiel a puits multiples. On etudie le comportement des valeurs propres qui tendent vers un niveau d'energie donne E 0 ∈R quand h→0
529 citations
TL;DR: In this paper, strong convergence results for nonlinear partial differential equaitons and minimization problems were proved for weakly convex hulls with σ-complete measure and complete measure.
Abstract: Let Ωbe endowed with a σ—, complete measure and let weakly in . If u(x) is an external point of the closed convex hull of a.e. in Ω, then strongly in cannot oscillate around u(x). Other strong convergence results are proved. Applications to the solution of nonlinear partial differential equaitons and of minimization problems are given.
179 citations
TL;DR: On etudie les proprietes des solutions globales pour le probleme suivant: ∂u/∂t-Δu+mu=g(u) dans R+XΩ, u=0 dans r+∂Ω ou ΩCR N est un ouvert borne regulier, g∈C(R,R) et m>γ 1, γ 1 etant la premiere valeur propre de −Δ dans H o 1 (Ω) as mentioned in this paper.
Abstract: On etudie les proprietes des solutions globales pour le probleme suivant: ∂u/∂t-Δu+mu=g(u) dans R+XΩ, u=0 dans R+∂Ω, ou ΩCR N est un ouvert borne regulier, g∈C(R,R) et m>γ 1 , γ 1 etant la premiere valeur propre de −Δ dans H o 1 (Ω)
121 citations
TL;DR: In this paper, the authors studied differentiability properties of functions belonging to the space generated by the vector fields in a J J Dx.connected open subset of Rn ; here the λjs are continuous (but in general not smooth) and nonnegative.
Abstract: In the first part of this paper we study some differentiabilityperties properties (In Sobolev space setting)of functions belonging to thespace generated by the vector fields in aJ J Dx.connected open subset of Rn ; here the λjs are continuous (but in generalnot smooth) and nonnegative. In particular, under suitable geometricalhypotheses involving the integral curves of we get thenfollowing embedding estimate: for all test functions u and for suitable positive constants e and CP depending only on the "order of degeneration" of the vector fields Such a problem arises naturally in study of the pointewise estimates for the weak solutions of some degenerate elliptic equations with measurable coefficients.
108 citations
TL;DR: In this article, the authors considered hypersurfaces in IRn+1 with prescribed gaussian curvature and related equations of monge-ampere type and showed that the curvature of the hypersurface can be modelled as a monge.
Abstract: (1984). Hypersurfaces in IRn+1 with prescribed gaussian curvature and related equations of monge—ampere type. Communications in Partial Differential Equations: Vol. 9, No. 8, pp. 807-838.
94 citations
TL;DR: Etude des proprietes des solutions de l'equation modelisant l'ecoulement d'un gaz dans un milieu poreux as mentioned in this paper.
Abstract: Etude des proprietes des solutions de l'equation modelisant l'ecoulement d'un gaz dans un milieu poreux
82 citations
TL;DR: On considere le probleme aux valeurs propres parabolique lineaire Lu=λmu dans Ω×R, u=0 sur ∂Ω× R, u(., 0)=u(., T) sur Ω et des generalisations non lineaires.
Abstract: On considere le probleme aux valeurs propres parabolique lineaire Lu=λmu dans Ω×R, u=0 sur ∂Ω×R, u(., 0)=u(., T) sur Ω et des generalisations non lineaires. L=∂/∂t+A(x, t, D), Ω⊂R N (N≥1) ∂Ω de classe C 2+ μ
74 citations
TL;DR: In this article, a Harnack inequality for degenerate parabolic equations is proposed for partial differential equations, which is a generalization of the one we consider in this paper. pp. 719-749.
Abstract: (1984). A Harnack inequality for degenerate parabolic equations. Communications in Partial Differential Equations: Vol. 9, No. 8, pp. 719-749.
72 citations
TL;DR: In this article, the authors consider le problem aux valeurs initiales suivant: v t −6vv x +v xxx = 0, v(x,0)=v(x) quand le profil initial v est asymptotique a des constantes differentes quand x→−∞ and x→+∞
Abstract: On considere le probleme aux valeurs initiales suivant: v t −6vv x +v xxx =0, v(x,0)=v(x) quand le profil initial v est asymptotique a des constantes differentes quand x→−∞ et x→+∞
45 citations
TL;DR: In this paper, regularite gevrey 3 pour la diffraction is used for diffraction in Partial Differential Equations (PDE) in the context of communication in partial differential equations.
Abstract: (1984). Regularite gevrey 3 pour la diffraction. Communications in Partial Differential Equations: Vol. 9, No. 15, pp. 1437-1494.
40 citations
TL;DR: In this article, a systeme d'equations aux derivees partielles lie aux equations d'Euler, and les resultats de regularite classiques for les equations elliptiques are derived.
Abstract: On etend les resultats de regularite classiques pour les equations elliptiques a un systeme d'equations aux derivees partielles lie aux equations d'Euler
TL;DR: The calculus of pseudo-differential operators of fuchs type as mentioned in this paper is a type of partial differential equation that is related to the calculus of partial differentials of pseudo differential operators of Fuchs type.
Abstract: (1984). The calculus of pseudo—differential operators of fuchs type. Communications in Partial Differential Equations: Vol. 9, No. 12, pp. 1179-1236.
TL;DR: A Concise Presentation of the Euler Equations of Hydrodynamics is given in this article, where the authors present a complete version of the complete Euler equation.
Abstract: (1984). A Concise Presentation of the Euler Equations of Hydrodynamics. Communications in Partial Differential Equations: Vol. 9, No. 6, pp. 539-559.
TL;DR: In this article, a semi-classical bound on the boundary values to the positive axis of R(z;H(h)) of the Schrodinger opera-tor is given.
Abstract: Let be the Schrodinger opera¬tor and denote by R(z;H(h)), Im≠O , the resolvent of H(h). The object of the present paper is twofold: (i) We give semi-classical bounds on the boundary values to the positive axis of R(z;H(h)); (ii) As an application of (i), we find the coupleteasymptotics of scattering phases as
TL;DR: Soit M une variete de Riemann compacte et Δ son operateur de Laplace-Beltrami Soit l'operateur de Schrodinger Hq=−Δ+q pour q∈C ∞ (M) Soit Is(q) l'ensemble des potentiels isospectraux a q On demontre que Is (q) est compact dans C ∞(M) si dim M≤3
Abstract: Soit M une variete de Riemann compacte et Δ son operateur de Laplace-Beltrami Soit l'operateur de Schrodinger Hq=−Δ+q pour q∈C ∞ (M) Soit Is(q) l'ensemble des potentiels isospectraux a q On demontre que Is(q) est compact dans C ∞ (M) si dim M≤3
TL;DR: Soit P (x, D) un operateur aux derivees partielles d'ordre m. On considere le probleme de Cauchy P(x,D)u=f, suppaC {x 1 ≥ 0} dans le cadre de C ∞, ou suppf⊂{x 1 − 0}. On donne des estimations des ensembles front d'onde des solutions de ce probleme as mentioned in this paper.
Abstract: Soit P (x, D) un operateur aux derivees partielles d'ordre m. On considere le probleme de Cauchy P (x, D)u=f, suppaC {x 1 ≥0} dans le cadre de C ∞ , ou suppf⊂{x 1 ≥0}. On donne des estimations des ensembles front d'onde des solutions de ce probleme de Cauchy
TL;DR: The authors construit la solution fondamentale de l'equation de la chaleur for le ∂ b -laplacien □ b sur une CR-variete compacte, pseudoconvexe equipee d'une metrique appropriee.
Abstract: On construit la solution fondamentale de l'equation de la chaleur pour le ∂ b -laplacien □ b sur une CR-variete compacte, fortement pseudoconvexe equipee d'une metrique appropriee
TL;DR: On considere le probleme de Cauchy pour une equation de type Schrodinger Lu(x,t)=(i∂ t +Δ+∑ j=1 m b j (x)∂x j +c(x)) u(ex,t)=f(x,t) dans R x m ×[0,T] (0
Abstract: On considere le probleme de Cauchy pour une equation de type Schrodinger Lu(x,t)=(i∂ t +Δ+∑ j=1 m b j (x)∂x j +c(x)) u(x,t)=f(x,t) dans R x m ×[0,T] (0
TL;DR: In this paper, it was shown that for any dimension and any m ≥ 1, the Dirichlet boundary value problem has compact support, and that no symmetry hypothese is made.
Abstract: We prove that if 1
TL;DR: In this article, the Evolution D'une Interface par diffusion de surface (EDI-surface) is described and discussed in the context of Partial Differential Equations (PDE).
Abstract: (1984). Evolution D'une Interface par diffusion de surface. Communications in Partial Differential Equations: Vol. 9, No. 4, pp. 313-335.
TL;DR: In this article, the pababolic oblique derivative problem with holder continuous coefficients was studied and a pababolic ODE was solved with pabolic oblique derivatives.
Abstract: (1984). On pababolic oblique derivative problem with holder continuous coefficients. Communications in Partial Differential Equations: Vol. 9, No. 14, pp. 1323-1372.
TL;DR: In this paper, the equations of the two-component theory in magnetohydrodynamics were studied and discussed in the context of partial differential equations (PDE) in the literature.
Abstract: (1984). On the equations of the two-component theory in magnetohydrodynamics. Communications in Partial Differential Equations: Vol. 9, No. 6, pp. 503-522.
TL;DR: In this article, the authors considered the Dirichlet problem in terms of the solutions of Dirichlets, and the comportement asymptotique des solutions, quand e→o(x).
Abstract: Soit Ω un ouvert de R m a frontiere lisse ∂Ω. On considere les solutions du probleme de Dirichlet eΔu+Σ 1=1 m b i u xi +(cu=0) dans Ω u/ ∂Ω =φ(x). On etudie le comportement asymptotique des solutions ue(x) quand e→o
TL;DR: In this article, a non lineaire elliptique equation non-lineaire is proposed, which is a solution unique sous certain hypotheses, and a methode de programmation dynamique.
Abstract: L'etude de problemes de commande optimale stochastique de processus de diffusion controles a la fois par impulsions et de facon continue, et arretes a la frontiere d'une region bornee de R N , conduit par une methode de programmation dynamique, a une equation non lineaire elliptique. On montre que cette equation a une solution unique sous certaines hypotheses
TL;DR: In this article, a kovalevskian system with time-dependent coefficients is presented, where the coefficients are derived from the time-varying coefficients of the kovaleskians.
Abstract: (1984). Ar kovalevskian systems with time-dependent coefficients. Communications in Partial Differential Equations: Vol. 9, No. 14, pp. 1373-1406.
TL;DR: Soit M une variete de Riemann complete. Valeurs propres en dessous du spectre essentiel, estimations L 2. Valeurs prores discretes.
Abstract: Soit M une variete de Riemann complete. Valeurs propres en dessous du spectre essentiel, estimations L 2 . Valeurs propres discretes. Estimation L infini des formes propres
TL;DR: In this article, the propagation de l'analycite (et du support) for les solutions assez regulieres d'equations aux derivees partielles non lineaires is discussed.
Abstract: On etudie la propagation de l'analycite (et du support) pour les solutions assez regulieres d'equations aux derivees partielles non lineaires. On montre que l'analycite se propage a travers des surfaces que les caracteristiques reelles de l'operateur linearise coupent transversalement