Search results for "UNIQUE"
showing 10 items of 268 documents
Existence and uniqueness for a degenerate parabolic equation with đżÂč-data
1999
In this paper we study existence and uniqueness of solutions for the boundary-value problem, with initial datum in L 1 ( Ω ) L^{1}(\Omega ) , u t = d i v a ( x , D u ) in ( 0 , â ) à Ω , \begin{equation*}u_{t} = \mathrm {div} \mathbf {a} (x,Du) \quad \text {in } (0, \infty ) \times \Omega , \end{equation*} â â u â η a â ÎČ ( u ) on ( 0 , â ) Ă â Ω , \begin{equation*}-{\frac {{\partial u} }{{\partial \eta _{a}}}} \in \beta (u) \quad \text {on } (0, \infty ) \times \partial \Omega ,\end{equation*} u ( x , 0 ) = u 0 ( x ) in Ω , \begin{equation*}u(x, 0) = u_{0}(x) \quad \text {in }\Omega ,\end{equation*} where a is a CarathĂ©odory function satisfying the classical Leray-Lions hypothesis, â / âŠ
On the notion of parallel transport on RCD spaces
2019
We propose a general notion of parallel transport on RCD spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space. peerReviewed
The Poisson embedding approach to the CalderĂłn problem
2020
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calder\'on type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result by Lassas and Uhlmann (2001) solving the Calder\'on problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.
Behandlung eines Goursatproblems mit einer verallgemeinerten Riemannschen Methode
1973
In dieser Arbeit wird ein lineares Goursat problem in zwei Zeit- und einer Raumvariablen behandelt. Die Koeffizienten der betrachteten Differentialgleichung mussen hierbei nach allen Variablen beliebig oft differenzierbar sein und nebst all ihren partiellen Ableitungen bestimmten Wachstumsbeschrankungen genugen. Fur die Inhomogenitat und die Vorgaben werden gesonderte Voraussetzungen gestellt. Zuerst wird fur ein hinsichtlich der Anfangsbedingungen verallgemeinertes Goursatproblem die eindeutige Losbarkeit in der gleichen Funktionenklasse bewiesen, in der die Koeffizienten der Differentialgleichung liegen. Auf Grund dieses Ergebnisses gelingt es dann, mit Hilfe einer verallgemeinerten RiemaâŠ
Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential
2020
AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the AmbrosettiâRabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λâRwhich we specify exactly in terms of principal eigenvalue of the differential operator.
The Configuration of Space Through Architecture in the Thinking of Gadamer
2017
Although Gadamer stresses the importance of temporality, historicity and tradition, the aim of this contribution is to underline the uniqueness of architecture in Truth and Methodsâ investigation relative to the essence of a work of art. The uniqueness of architecture for Gadamer lies not only in the fact that it gives space for the expression of all other kinds of artworks; a building has to be to understood as self-sufficient and as autarchic, but also as inscribed in the concrete historical life. A further aspect of the uniqueness of architecture originates in the fact that a building determines our way of life or our dwelling even in a political sense.
On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients
2017
International audience; The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space problem we establish energy estimates with finite loss of derivatives, which is linearly increasing in time. This implies well-posedness in H â , if the coefficients enjoy enough smoothness in x. From this result, by standard arguments (i.e. extension and convexification) we deduce also local existence and uniqueness. A huge part of the analysis is devoted to give an appropriate sense to the Cauchy problem, which is not evideâŠ
Greenâs function and existence of solutions for a third-order three-point boundary value problem
2019
The solutions of third-order three-point boundary value problem xâââ + f(t, x) = 0, t â [a, b], x(a) = xâ(a) = 0, x(b) = kx(η), where η â (a, b), k â R, f â C([a, b] Ă R, R) and f(t, 0) â 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Greenâs function. As an application, also one example is given to illustrate the result. Keywords: Greenâs function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.
Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type
2021
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rusâs fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets
2004
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.