On the best Hölder exponent for two dimensional elliptic equations in divergence form

We obtain an estimate for the Hölder continuity exponent for weak solutions to the following elliptic equation in divergence form:

where is a bounded open subset of and, for every , is a symmetric matrix with bounded measurable coefficients. Such an estimate ``interpolates' between the well-known estimate of Piccinini and Spagnolo in the isotropic case , where is a bounded measurable function, and our previous result in the unit determinant case . Furthermore, we show that our estimate is sharp. Indeed, for every we construct coefficient matrices such that is isotropic and has unit determinant, and such that our estimate for reduces to an equality, for every .

     

Clustering space-time series: FSTAR as a flexible STAR approach

Advances in Data Analysis and Classification - The STAR model is widely used to represent the dynamics of a certain variable recorded at several locations at the same time. Its advantages are often...     

On the Green Function of the Annulus

Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.     

Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

Blocking Sets of Certain Line Sets Related to a Conic

In this paper we classify point sets of minimum size of two types (1) point sets meeting all secants to an irreducible conic of the desarguesian projective plane PG(2,q), q odd; (2) point sets meeting all external lines and tangents to a given irreducible conic of the desarguesian projective plane PG(2,q), q even.     

On a discrimination problem for a class of stochastic processes with ordered first‐passage times

Consider the Bayes problem in which one has to discriminate if the random unknown initial state of a stochastic process is distributed according to either of two preassigned distributions, on the base of the observation of the first‐passage time of the process through 0. For processes whose first‐passage times to state 0 are increasing in the initial state according to the likelihood ratio order, such problem is solved by determining the Bayes decision function and the corresponding Bayes error. The special case of fixed initial values including a family of first‐passage times with proportional reversed hazard functions is then studied. Finally, various applications to birth‐and‐death and to diffusion processes are discussed. Copyright © 2001 John Wiley & Sons, Ltd.