Let Ω be a smooth open bounded set in RN, let ϱ be the (smoothed in the interior) distance function from ∂Ω, let (aij) be a uniformly elliptic matrix with continuous entries in Ω and A the associated second order elliptic operator. Under... more
Let Ω be a smooth open bounded set in RN, let ϱ be the (smoothed in the interior) distance function from ∂Ω, let (aij) be a uniformly elliptic matrix with continuous entries in Ω and A the associated second order elliptic operator. Under suitable conditions, we prove that the operator L=−ϱA+B, with B a first order operator with continuous coefficients,
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We give estimates on the bottom of the essential spectrum of Schrodinger operators +V in L2(RN ).
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We consider a strictly elliptic operatorAu=∑ijDi(aijDju)−b⋅∇u+div(c⋅u)−Vu, where 0⩽V∈Lloc∞, aij∈Cb1(RN), b,c∈C1(RN,RN). If divb⩽βV, divc⩽βV, 0β1, then a natural realization of A generates a positive C0-semigroup T in L2(RN). The semigroup... more
We consider a strictly elliptic operatorAu=∑ijDi(aijDju)−b⋅∇u+div(c⋅u)−Vu, where 0⩽V∈Lloc∞, aij∈Cb1(RN), b,c∈C1(RN,RN). If divb⩽βV, divc⩽βV, 0β1, then a natural realization of A generates a positive C0-semigroup T in L2(RN). The semigroup satisfies pseudo-Gaussian estimates if|b|⩽k1Vα+k2,|c|⩽k1Vα+k2, where 12⩽α1. If α=12, then Gaussian estimates are valid. The constant α=12 is optimal with respect to this property.
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We study global regularity properties of transitions kernels associated with second-order differential operators in R N with unbounded drift and potential terms. Under suitable conditions, we prove Sobolev regularity of transition kernels... more
We study global regularity properties of transitions kernels associated with second-order differential operators in R N with unbounded drift and potential terms. Under suitable conditions, we prove Sobolev regularity of transition kernels and pointwise upper bounds. As an application, we obtain sufficient conditions implying the differentiability of the associated semigroup on the space of bounded and continuous functions on R
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We give sufficient conditions for the discreteness of the spectrum of differentialoperators of the form Au = \Gamma\Deltau +hrF;rui in L2 (Rn) where d(x) = e\GammaF (x)dx andfor Schrodinger operators in L2(Rn). Our conditions are also... more
We give sufficient conditions for the discreteness of the spectrum of differentialoperators of the form Au = \Gamma\Deltau +hrF;rui in L2 (Rn) where d(x) = e\GammaF (x)dx andfor Schrodinger operators in L2(Rn). Our conditions are also necessary in the case ofpolynomial coefficients.Mathematics subject classification (1991): 35P05, 35J10, 35J701 IntroductionIn this paper we study the discreteness of the spectrum of two
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... Luigi Ambrosio Dipartimento di Matematica \F. Casorati", Via Abbiategrasso 205 27100 Pavia, Italy Nicola Fusco Dipartimento di Matematica \U. Dini", Viale Morgagni 67/A 50134 Firenze, Italy Diego Pallara Dip.... more
... Luigi Ambrosio Dipartimento di Matematica \F. Casorati", Via Abbiategrasso 205 27100 Pavia, Italy Nicola Fusco Dipartimento di Matematica \U. Dini", Viale Morgagni 67/A 50134 Firenze, Italy Diego Pallara Dip. di Matematica Universit a di Lecce CP 193, 73100 Lecce, Italy ...
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We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order dierential operators in RN with unbounded drift. As an application, we obtain sucient conditions implying the... more
We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order dierential operators in RN with unbounded drift. As an application, we obtain sucient conditions implying the dierentiability
Let aij 2 C1 b(R
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The sector of analyticity of the Ornstein-Uhlenbeck semigroup is computed on the space Lp µ := Lp (RN ; µ) with respect to its invariant measure µ .I fA =∆ +Bx ·∇ denotes the generator of the Ornstein-Uhlenbeck semigroup, then the angle... more
The sector of analyticity of the Ornstein-Uhlenbeck semigroup is computed on the space Lp µ := Lp (RN ; µ) with respect to its invariant measure µ .I fA =∆ +Bx ·∇ denotes the generator of the Ornstein-Uhlenbeck semigroup, then the angle θ2 of the sector of analyticity in L2 µ is π/2 minus the spectral angle of BQ∞, Q∞
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Let A=∑i,j=1NqijDij+∑i,j=1NbijxjDi be a possibly degenerate Ornstein–Uhlenbeck operator in RN and assume that the associated Markov semigroup has an invariant measure μ. We compute the spectrum of A in Lμp for 1⩽p<∞.
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We study the generation of an analytic semigroup in Lp(Rd) and the de- termination of the domain for a class of second order elliptic operators with unbounded coecien ts in Rd. We also establish the maximal regularity of type Lq{Lp for... more
We study the generation of an analytic semigroup in Lp(Rd) and the de- termination of the domain for a class of second order elliptic operators with unbounded coecien ts in Rd. We also establish the maximal regularity of type Lq{Lp for the corre- sponding inhomogeneous parabolic equation. In contrast to the previous literature the coecien ts of the second derivatives
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We prove sharp upper bounds for invariant measures of Markov processes inNassociated with second-order elliptic differential operators with unbounded coefficients.
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Functions of bounded variation in an abstract Wiener space, i.e., an infinite-dimensional Banach space endowed with a Gaussian measure and a related differential structure, have been introduced by M. Fukushima and M. Hino using Dirichlet... more
Functions of bounded variation in an abstract Wiener space, i.e., an infinite-dimensional Banach space endowed with a Gaussian measure and a related differential structure, have been introduced by M. Fukushima and M. Hino using Dirichlet forms, and their properties have been studied with tools from analysis and stochastics. In this paper we reformulate, in an integral-geometric vein and with purely
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Given a second-order degenerate ordinary differential operator A in a real interval, we study the generation of a strongly continuous semigroup in spaces of continuous functions under Neumann-type boundary conditions and the existence of... more
Given a second-order degenerate ordinary differential operator A in a real interval, we study the generation of a strongly continuous semigroup in spaces of continuous functions under Neumann-type boundary conditions and the existence of classical solutions of the associated parabolic initial value problem.