Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerate-elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance, generators of diffusion processes arising in mathematical biology, and the study of porous media.Comment: 58 pages, 1 figure. To appear in the Journal of Differential Equations. Incorporates final galley proof corrections corresponding to published versio

Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions

We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our article focuses on the Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance and a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate, elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to terminal/boundary value or obstacle problems for the parabolic Heston operator correspond to value functions for American-style options on the underlying asset.Comment: 47 pages; to appear in Transactions of the American Mathematical Societ

A HOLISTIC APPROACH OF RELATIONSHIP MARKETING IN LAUNCHING LUXURY NEW PRODUCTS

On the basis of increased complexity of the exchange mechanism, at the beginning of the third millennium the contemporary marketing suffers some physiognomic changes. Holistic orientation of the contemporary marketing is imposed by the new dimensions therelationship marketing, holistic marketing, luxury marketing, residential complex, research on perception of luxury

New rr-Matrices for Lie Bialgebra Structures over Polynomials

For a finite dimensional simple complex Lie algebra $\mathfrak{g}$, Lie bialgebra structures on $\mathfrak{g}[[u]]$ and $\mathfrak{g}[u]$ were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to produce $r$-matrices which correspond to Lie bialgebra structures over polynomials

Chiral molecular conductors based on methylated TTF derivatives

International audienc

Straightforward synthesis and insights of the photophysical properties of tetrathiafulvalene-acceptors (TTF-A)

International audienc

THE EVOLUTION OF AGRICULTURAL SURFACES, BY USE CATEGORIES, IN THE SW AND NW REGIONS OF ROMANIA

The paper analyzes the evolution after 1990 of the areas occupied by categories of agricultural use, in the NW and SW development regions of Romania. The areas occupied by agricultural land had similar evolutions, with some small exceptions, due primarily to the predominant landforms in the two analyzed development regions. The data are incomplete, waiting for the conclusion of the National Cadastre and Land Book Program 2015-2023