### A comparison principle for an American option on several assets: index and spread options.

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We prove a generalized maximum principle for subsolutions of boundary value problems, with mixed type unilateral conditions, associated to a degenerate parabolic second-order operator in divergence form.

The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures. The solution is defined via a variational inequality, following Temam?s technique for the evolution problem...

Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p > 2), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in N-dimension) and therefore its Hausdorff dimension is less than N. In particular the N-Lebesgue measure of the free boundary is zero for each t-level.

In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form $b\left(u\right)$, where $b\in {L}_{\mathrm{loc}}^{\infty}\left(R\right).$ Extending $b$ to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.

In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.

In this paper we study a class of abstract quasi-variational inequalities with nonlocal constraints depending on the unknown and establish an existence result. Further we give its applications to parabolic systems of partial differential inequalities with nonlocal obstacles depending on the unknowns.

We prove ${H}_{loc}^{1}$-regularity for the stresses in the Prandtl-Reuss-law. The proof runs via uniform estimates for the Norton-Hoff-approximation.

This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...