We prove boundedness of minimizers of energy-functionals, for instance of the anisotropic type (1.1) below, under sharp assumptions on the exponents pi in terms of p ∗: the Sobolev conjugate exponent of p; i.e., p∗ = np n−p , 1 p = 1 n Pn i=1 1 pi . As a consequence, by mean of regularity results due to Lieberman [21], we obtain the local Lipschitz-continuity of minimizers under sharp assumptio...

In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideal...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

The asymptotic properties of the maximum likelihood and bayesian estimators of finite dimensional parameters of any statistical model depend strongly on the regularity conditions. It is well-known that if these conditions are fulfilled then the estimators are consistent, asymptotically normal and asymptotically efficient. These regularity conditions are of the following type: the model is suffi...