St. Petersburg Mathematical Journal Template

Paolo Baroni, Maria Colombo, Giuseppe Mingione · 30 Mar 2016

The class of non-autonomous functionals under study is characterized by the fact that the energy density changes its ellipticity and growth properties according to the point; some regularity results are proved for related minimizers. These results are the borderline counterpart of analogous ones previously derived for non-autonomous functionals with $(p,q)$-growth. Also, similar functionals related to…

M. Sh. Birman, T. A. Suslina · 2 Aug 2004

The vector periodic differential operators (DO’s) $\mathcal {A}$ admitting a factorization ${\mathcal {A}}={\mathcal {X}} ^*{\mathcal {X}}$, where $\mathcal {X}$ is a first order homogeneous DO, are considered in $L_2(\mathbb {R}^d)$. Many operators of mathematical physics have this form. The effects that depend only on a rough behavior of the spectral expansion of $\mathcal {A}$ in…

Askold Khovanskiĭ · 1 Jan 1993

V. P. Spiridonov · 16 Nov 2004

A general class of (multiple) hypergeometric type integrals associated with the Jacobi theta functions is defined. These integrals are related to theta hypergeometric series via the residue calculus. In the one variable case, theta function extensions of the Meijer function are obtained. A number of multiple generalizations of the elliptic beta integral associated with the…

M. Sh. Birman, T. A. Suslina · 21 Sep 2006

We continue to study the class of matrix periodic elliptic differential operators ${{\mathcal {A}}_\varepsilon }$ in ${\mathbb {R}^d}$ with coefficients oscillating rapidly (i.e., depending on ${{\mathbf {x}}/\varepsilon }$). This class was introduced in the authors’ earlier work of 2001 and 2003. The