We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient and surrounded by host tissue. The introduction of cytotoxic drugs into the system serves to eliminate the tumor cells and in this setting the concentration o...

This paper summarizes as a working paperbasic facts in both nite and in nite dimensional optimization in view of optimality conditions and stability of solutions to perturbed problems. Begining with section 4, partially new and unpublished results are included, elaborated in joint work with D. Klatte, Univ. Zuerich.

We study optimal control problems of systems describing the flow of incompressible shear-thickening fluids. We prove existence of solutions and derive necessary optimality conditions under precise restrictions on the optimal control.

This paper presents a parameterized family of equilibrium strategy profiles for three-player Kuhn poker. This family illustrates an important feature of three-player equilibrium profiles that is not present in two-player equilibrium profiles the ability of one player to transfer utility to a second player at the expense of the third player, while playing a strategy in the profile family. This f...

We consider nonlinear elliptic equations with small diffusion and Dirichlet boundary conditions. We construct changing sign solutions with peaks close to the boundary and consider the location of the peak.

| Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. Th...

A binary matrix has the consecutive ones property (C1P) if it is possible to order the columns so that all 1s are consecutive in every row. In [McConnell, SODA 2004 768-777] the notion of incompatibility graph of a binary matrix was introduced and it was shown that odd cycles of this graph provide a certificate that a matrix does not have the consecutive ones property. A bound of k + 2 was clai...

We consider semilinear elliptic problems of the form ∆u+g(u) = f(x) with Neumann boundary conditions or ∆u + λ1u + g(u) = f(x) with Dirichlet boundary conditions, and we derive conditions on g and f under which an upper bound on the number of solutions can be obtained.