共查询到20条相似文献,搜索用时 31 毫秒
1.
Angelo Alvino 《Journal of Differential Equations》2010,249(12):3279-3290
We prove a comparison principle for second order quasilinear elliptic operators in divergence form when a first order term appears. We deduce uniqueness results for weak solutions to Dirichlet problems when data belong to the natural dual space. 相似文献
2.
We study the Cauchy problem for time-dependent diffusion operators with singular coefficients on L1-spaces induced by infinitesimal invariant measures. We give sufficient conditions on the coefficients such that the Cauchy-Problem is well-posed. We construct associated diffusion processes with the help of the theory of generalized Dirichlet forms. We apply our results in particular to construct a large class of Nelson-diffusions that could not been constructed before. 相似文献
3.
Scott N. Armstrong 《Journal of Differential Equations》2009,247(3):931-955
We generalize the Donsker-Varadhan minimax formula for the principal eigenvalue of a uniformly elliptic operator in nondivergence form to the first principal half-eigenvalue of a fully nonlinear operator which is concave (or convex) and positively homogeneous. Examples of such operators include the Bellman operator and the Pucci extremal operators. In the case that the two principal half-eigenvalues are not equal, we show that the measures which achieve the minimum in this formula provide a partial characterization of the solvability of the corresponding Dirichlet problem at resonance. 相似文献
4.
Small time asymptotics of diffusion processes 总被引:1,自引:0,他引:1
We establish the short-time asymptotic behaviour of the Markovian semigroups associated with strongly local Dirichlet forms
under very general hypotheses. Our results apply to a wide class of strongly elliptic, subelliptic and degenerate elliptic
operators. In the degenerate case the asymptotics incorporate possible non-ergodicity. 相似文献
5.
Niels Jacob 《Potential Analysis》1992,1(3):221-232
It is shown that a special class of symmetric elliptic pseudo differential operators do generate a Feller semigroup and therefore a non-local Dirichlet form. 相似文献
6.
Nina Zorboska 《Proceedings of the American Mathematical Society》1998,126(7):2013-2023
We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.
7.
We study absolute-continuity relationships for a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to the law of the original process and we compute explicitly the associated Radon–Nikodym densities. This work unifies and generalizes to random non-linear transformations several previous quasi-invariance results for gamma and Dirichlet processes. 相似文献
8.
Dirichlet空间上的Bergman型Toeplitz算子 总被引:1,自引:1,他引:0
本文给出了Dirichlet空间上以有界调和函数为符号的Bergman型Toeplitz算子是紧算子的充要条件.同时刻画了此类Bergman型Toeplitz算子在Dirichlet空间上的交换性. 相似文献
9.
In this paper, we define the discrete p-Schrödinger operators on finite networks and discuss the existence of the Dirichlet eigenvalues and their eigenfunctions for the operators. We also provide various equivalent conditions for the existence of positive solutions for Dirichlet boundary value problems for the operators. 相似文献
10.
On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero. 相似文献
11.
We give a sufficient condition for essential self-adjointness of symmetric operators associated with classical Dirichlet forms on Hilbert spaces. The condition implies a one-sided restriction on the derivatives for a suitable approximation of the drift coefficient but does not involve L
p
or smoothness conditions on .Supported by the Alexander von Humboldt Foundation. 相似文献
12.
Paolo Salani 《Applicable analysis》2013,92(12):1185-1197
We investigate how some geometric properties of the domain are inherited by level sets of solutions of elliptic equations. In particular we prove that, under suitable assumptions, solutions of elliptic Dirichlet problems in starshaped rings have starshaped level sets. Our results are applicable to a large class of operators, including fully-nonlinear ones. 相似文献
13.
Mathematical Notes - We study the Dirichlet problem in a half-space for elliptic differential-difference equations with operators that are compositions of differential operators and shift operators... 相似文献
14.
Olaf Post 《Mathematische Nachrichten》2016,289(8-9):1052-1099
We introduce a purely functional analytic framework for elliptic boundary value problems in a variational form. We define abstract Neumann and Dirichlet boundary conditions and a corresponding Dirichlet‐to‐Neumann operator, and develop a theory relating resolvents and spectra of these operators. We illustrate the theory by many examples including Jacobi operators, Laplacians on spaces with (non‐smooth) boundary, the Zaremba (mixed boundary conditions) problem and discrete Laplacians. 相似文献
15.
Summary We study Dirichlet forms associated with random walks on fractal-like finite grahs. We consider related Poincaré constants and resistance, and study their asymptotic behaviour. We construct a Markov semi-group on fractals as a subsequence of random walks, and study its properties. Finally we construct self-similar diffusion processes on fractals which have a certain recurrence property and plenty of symmetries.Partly supported by the JSPS Program 相似文献
16.
Michael Röckner 《Journal of Functional Analysis》2003,203(1):237-261
Harnack inequalities are established for a class of generalized Mehler semigroups, which in particular imply upper bound estimates for the transition density. Moreover, Poincaré and log-Sobolev inequalities are proved in terms of estimates for the square field operators. Furthermore, under a condition, well-known in the Gaussian case, we prove that generalized Mehler semigroups are strong Feller. The results are illustrated by concrete examples. In particular, we show that a generalized Mehler semigroup with an α-stable part is not hyperbounded but exponentially ergodic, and that the log-Sobolev constant obtained by our method in the special Gaussian case can be sharper than the one following from the usual curvature condition. Moreover, a Harnack inequality is established for the generalized Mehler semigroup associated with the Dirichlet heat semigroup on (0,1). We also prove that this semigroup is not hyperbounded. 相似文献
17.
We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups.
Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued
processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the
problem. Comparison and global properties of solutions are also studied.
Accepted 29 August 2001. Online publication 17 December 2001. 相似文献
18.
Summary. In this paper, we show the convergence of forms in the sense of Mosco associated with the part form on relatively compact
open set of Dirichlet forms with locally uniform ellipticity and the locally uniform boundedness of ground states under regular
Dirichlet space setting. We also get the same assertion under Dirichlet space in infinite dimensional setting. As a result
of this, we get the weak convergence under some conditions on initial distributions and the growth order of the volume of
the balls defined by (modified) pseudo metric used in K. Th. Sturm.
Received: 18 September 1995 / In revised form: 23 January 1997 相似文献
19.
N. Balakrishnan 《Journal of multivariate analysis》2011,102(5):948-957
In this paper, we discuss some basic distributional and asymptotic properties of the Pearson-Kotz Dirichlet multivariate distributions. These distributions, which appear as the limit of conditional Dirichlet random vectors, possess many appealing properties and are interesting from theoretical as well as applied points of view. We illustrate an application concerning the approximation of the joint conditional excess distribution of elliptically symmetric random vectors. 相似文献
20.
Mathematical Notes - We study the Dirichlet problem in a half-space for elliptic differential-difference equations with operators representing superpositions of differential operators and... 相似文献