Elliptic Operators on Rd with Unbounded Coefficients

L^p-Regularity for Elliptic Operators with Unbounded Coefficients

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Analytic Semigroups and Degenerate Elliptic Operators with Unbounded Coefficients: A Probabilistic Approach

In the present paper we are dealing with generation of analytic semigroups in the space of continuous and bounded functions by suitable second order differential operators, which have unbounded coefficients and may be degenerate. This means that we are away from the classical framework in the study of the generation of analytic semigroups by elliptic operators (see Lunardi [25] for a comprehens...

Spectral Curves of Operators with Elliptic Coefficients⋆

The classical theory of reduction, initiated by Weierstrass, has found modern applications to the fields of Integrable Systems and Number Theory, to name but two. In this short note we only address specific cases, providing minimal historical references, listing the steps that we devised, and exhibiting some new explicit formulas. A full-length discussion of original motivation, theoretical adv...

L–regularity for Parabolic Operators with Unbounded Time–dependent Coefficients

We establish the maximal regularity for nonautonomous OrnsteinUhlenbeck operators in L-spaces with respect to a family of invariant measures, where p ∈ (1,+∞). This result follows from the maximal L-regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on L(R ) with Lebesgue measure.