Search results for "Uniqueness theorem for Poisson's equation"

The Homogeneous Poisson Point Process

2008

Erratum: An Inverse Backscatter Problem for Electric Impedance Tomography

2011

We fix an incorrect statement from our paper [M. Hanke, N. Hyvonen, and S. Reusswig, SIAM J. Math. Anal., 41 (2009), pp. 1948–1966] claiming that two different perfectly conducting inclusions necessarily have different backscatter in impedance tomography. We also present a counterexample to show that this kind of nonuniqueness does indeed occur.

Minimizing total variation flow

2000

We prove existence and uniqueness of weak solutions for the minimizing total variation flow with initial data in $L^1$. We prove that the length of the level sets of the solution, i.e., the boundaries of the level sets, decreases with time, as one would expect, and the solution converges to the spatial average of the initial datum as $t \to \infty$. We also prove that local maxima strictly decrease with time; in particular, flat zones immediately decrease their level. We display some numerical experiments illustrating these facts.

Global fixed point proof of time-dependent density-functional theory

2011

We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point question for potentials on a given time-interval. We show that the unique fixed point, i.e. the unique potential generating a given density, is reached as the limiting point of an iterative procedure. The one-to-one correspondence between densities and potentials is a straightforward result provided that the response function of the divergence of the internal forces is bounded. The existence, i.e. the v-representability of a density, can be proven as wel…

Radial growth of solutions to the poisson equation

2001

We establish a radial growth estimate of the type of the iterated law of the logarithm for solutions to the Poisson equation in the unit ball.

The Poisson Bracket Structure of the SL(2, R)/U(1) Gauged WZNW Model with Periodic Boundary Conditions

2000

The gauged SL(2, R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory. For periodic boundary conditions zero modes imply non-local Poisson brackets which, nevertheless, can be represented by canonical free fields.

Empirical measures and Vlasov hierarchies

2013

The present note reviews some aspects of the mean field limit for Vlasov type equations with Lipschitz continuous interaction kernel. We discuss in particular the connection between the approach involving the N-particle empirical measure and the formulation based on the BBGKY hierarchy. This leads to a more direct proof of the quantitative estimates on the propagation of chaos obtained on a more general class of interacting systems in [S.Mischler, C. Mouhot, B. Wennberg, arXiv:1101.4727]. Our main result is a stability estimate on the BBGKY hierarchy uniform in the number of particles, which implies a stability estimate in the sense of the Monge-Kantorovich distance with exponent 1 on the i…

Shakedown analysis for a class of strengthening materials within the framework of gradient plasticity

2010

Abstract The classical shakedown theory is extended to a class of perfectly plastic materials with strengthening effects (Hall–Petch effects). To this aim, a strain gradient plasticity model previously advanced by Polizzotto (2010) is used, whereby a featuring strengthening law provides the strengthening stress, i.e. the increase of the yield strength produced by plastic deformation, as a degree-zero homogeneous second-order differential form in the accumulated plastic strain with associated higher order boundary conditions. The extended static (Melan) and kinematic (Koiter) shakedown theorems are proved together with the related lower bound and upper bound theorems. The shakedown limit loa…