[PDF] Top 20 Some uniqueness results for Bernoulli interior free-boundary problems in convex domains

... show in Theorem ...(1.2). In fact the key point for the proof of Theorem ...Borell in [6], whereas for Theorem ...equality in Borell ...authors in [11]. Since the ... Voir le document complet

... Abstract In this paper, we firstly consider steady Euler flows in two-dimensional bounded annuli, as well as in complements of disks, in punctured disks and in the punctured ...wall ... Voir le document complet

... method for the approximation of a class of free boundary problems of Bernoulli’s type, reformulated as optimal shape design problems with appropriate shape ...admissible domains ... Voir le document complet

... and uniqueness results can be proved, which is true for the obstacle problem of Theorem 1 but is not known for more general problems ...the free boundary holds for ... Voir le document complet

... to uniqueness via Ishii’s implementation of Perron’s method ...out in two ...establish uniqueness and then existence by standard viscosity solutions the- ory (see Ishii and Lions [15] and [8]) even ... Voir le document complet

... “exterior Bernoulli problem”, since the boundary of the solution domain ∂A is exterior to the given domain ...The interior Bernoulli problem is similar, with A ⊂ Ω and then u defined (and ... Voir le document complet

... limits for porous medium equations with a source term. Such asymptotic problems give rise to free bound- aries, which, in the absence of active motion, are generalized Hele-Shaw ...flows. ... Voir le document complet

... necessary for uniqueness as counterexamples show (see [8], Example ...the interior Bernoulli problem is more delicate and not even convexity can ensure ...elliptic problems are solved ... Voir le document complet

... Incorporating boundary conditions at infinity into simulations on bounded com- putational domains is a repeatedly occurring problem in scientific ...and boundary element methods (BEM) is the ... Voir le document complet

... (existence, uniqueness, stability) was carried out by Beurling [6] and Flusher and ...Rumpf[3]. In particular the notion of elliptic, hyperbolic and parabolic solution is ...defined. In view of this, ... Voir le document complet

... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ... Voir le document complet

... The goal of this study is to better understand convex planar do- mains in which the billiard ball map is integrable, that is, where there is a continuous family [r] ... Voir le document complet

... Another result which generalizes Theorem 3.5 is described in the following the- orem. Theorem 3.7. Let f, h and g be three positive continuous functions and f ≤ h on [a, b]. Suppose that f h is decreasing, f and g ... Voir le document complet

... trivial. For the free Shr¨ odinger operator or operators with compactly supported potential a sharp analog of the Hardy un- certainty principle is ...employed for the case of general real-valued ... Voir le document complet

... shown, for the first time, that HL suffers from non-optimal con- vergence, compared to ABB and ...approximations for the auxiliary variable, but only at the cost of increased computational ...BMC for ... Voir le document complet

... introduced in [2] and fully developed in [39, 37], can be viewed as the probabilistic analogues of semi-linear partial differential equations ...(PDEs). In particular, BSDEs are used to describe the ... Voir le document complet

... Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Ir[r] ... Voir le document complet

... 2.1. In general there is a trade off between the regularity of the boundary ∂Ω and the generality and smoothness of the boundary condition G, see [1] for a ...compensates for very ... Voir le document complet

... Abstract: In this work we consider the optimal control problem of a semilinear elliptic PDE with a Dirichlet boundary condition, where the control variable is distributed over the domain and is constrained ... Voir le document complet

... Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Ir[r] ... Voir le document complet