Results 1 
7 of
7
The AllegrettoPiepenbrink Theorem for Strongly Local Dirichlet Forms
 DOCUMENTA MATH.
, 2009
"... The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator. ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.
Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
, 2009
"... We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples. ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples.
Inequalities of HardySobolev type in CarnotCarathéodory spaces
 In: “Sobolev Spaces in Mathematics I
, 2009
"... Abstract. We consider various types of HardySobolev inequalities on a CarnotCarathéodory space (Ω, d) associated to a system of smooth vector fields X = {X1, X2,..., Xm} on R n satisfying the Hörmander’s finite rank condition rank Lie[X1,..., Xm] ≡ n. One of our main concerns is the trace inequal ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We consider various types of HardySobolev inequalities on a CarnotCarathéodory space (Ω, d) associated to a system of smooth vector fields X = {X1, X2,..., Xm} on R n satisfying the Hörmander’s finite rank condition rank Lie[X1,..., Xm] ≡ n. One of our main concerns is the trace inequality Z ϕ(x)  p Z
A Green function and regularity results for an ultraparabolic equation with a singular potential
 Adv. in Diff. Eq
"... Abstract. We prove a Harnack inequality for the positive solutions of a Schrödinger type equation L0 u + V u = 0, where L0 is an operator satisfying the Hörmander’s condition and V belongs to a class of functions of StummelKato type. We also obtain the existence of a Green function and an uniquenes ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We prove a Harnack inequality for the positive solutions of a Schrödinger type equation L0 u + V u = 0, where L0 is an operator satisfying the Hörmander’s condition and V belongs to a class of functions of StummelKato type. We also obtain the existence of a Green function and an uniqueness result for the CauchyDirichlet problem. 1.
Harnack inequality and continuity of solutions to quasilinear degenerate parabolic equations with coefficients from Katotype classes
, 2009
"... ..."
Research Article Harnack Inequality for the Schrödinger Problem Relative to Strongly Local Riemannian pHomogeneous Forms with a Potential in the Kato Class
"... We define a notion of Kato class of measures relative to a Riemannian strongly local phomogeneous Dirichlet form and we prove a Harnack inequality (on balls that are small enough) for the positive solutions to a Schrödingertype problem relative to the form with a potential in the Kato class. Copy ..."
Abstract
 Add to MetaCart
(Show Context)
We define a notion of Kato class of measures relative to a Riemannian strongly local phomogeneous Dirichlet form and we prove a Harnack inequality (on balls that are small enough) for the positive solutions to a Schrödingertype problem relative to the form with a potential in the Kato class. Copyright © 2007 M. Biroli and S. Marchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
OSCILLATION ESTIMATES RELATIVE TO pHOMOGENEUOUS FORMS AND KATO MEASURES DATA
"... We state pointwise estimate for the positive subsolutions associated to a phomogeneous form and nonnegative Radon measures data. As a byproduct we establish an oscillation’s estimate for the solutions relative to Kato measures data. 1. Introduction. The necessary part of the Wiener criterion for t ..."
Abstract
 Add to MetaCart
(Show Context)
We state pointwise estimate for the positive subsolutions associated to a phomogeneous form and nonnegative Radon measures data. As a byproduct we establish an oscillation’s estimate for the solutions relative to Kato measures data. 1. Introduction. The necessary part of the Wiener criterion for the regularity of boundary points in the case of nonlinear elliptic problems has been proved in a recent paper by Malỳ, [15] [16], using an estimate on positive subsolutions of the problem. The estimate has been generalized