Bildsegmentation zur Untersuchung von Streulichtbildern bei der laseroptischen Diagnose von rheumatoider Arthritis

Optical imaging in biomedicine is governed by the light absorption and scattering interaction on microscopic and macroscopic constituents in the medium. Therefore, light scattering characteristics of human tissue correlates with the stage of some diseases. In the near infrared range the scattering event with the coefficient approximately two orders of magnitude greater than absorption plays a dominant role. The potential of an experimental laser diode based setup for the transillumination of rheumatoid finger joints and the pattern of the stray light detection are demonstrated. For evaluating the scattering light images a new non-local image segmentation method is presented. Regarding a noisy picture as a multicomponent mixture of gray scaled particles, this method minimizes a non-convex free energy functional under the constraint of mass conservation of the components. Contrary to constructing equilibrium distributions as steady states of an adequate evolution equation, a direct descent method for the free energy is used to separate the components of the image

Distributed optimal control of a nonstandard system of phase field equations

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by the same authors in arXiv:1103.4585v1 [math.AP] and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.Comment: Key words: distributed optimal control, nonlinear phase field systems, first-order necessary optimality condition

An application of the implicit function theorem to an energy model of the semiconductor theory

In this paper we deal with a mathematical model for the description of heat conduction and carrier transport in semiconductor heterostructures. We solve a coupled system of nonlinear elliptic differential equations consisting of the heat equation with Joule heating as a source, the Poisson equation for the electric field and drift-diffusion equations with temperature dependent coefficients describing the charge and current conservation, subject to general thermal and electrical boundary conditions. We prove the existence and uniqueness of Hoelder continuous weak solutions near thermodynamic equilibria points using the Implicit Function Theorem. To show the differentiability of maps corresponding to the weak formulation of the problem we use regularity results from the theory of nonsmooth linear elliptic boundary value problems in Sobolev-Campanato spaces. (orig.)SIGLEAvailable from TIB Hannover: RR 5549(333)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

THE SQUARE ROOT PROBLEM FOR SECOND ORDER, DIVERGENCE FORM OPERATORS WITH MIXED BOUNDARY CONDITIONS ON L p

Abstract. We show that, under very general conditions on the domain Ω and the Dirichlet partD of the boundary, the operator ( −∇·µ∇+1) 1/2 with mixed boundary conditions provides a topological isomorphism between W 1,p D (Ω) and Lp (Ω), if p ∈]1,2]. hal-00737614, version 2- 23 Jan 201