共查询到20条相似文献,搜索用时 15 毫秒
1.
I. M. Oleinik 《Proceedings of the American Mathematical Society》1999,127(3):889-900
In this paper, we give sufficient conditions for the essential self-adjointness of second order elliptic operators. It turns out that these conditions coincide with those for the Schrödinger operator on a manifold whose metric essentially depends on the principal coefficients of a given operator.
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The purpose of the present paper is to discuss the role of second order elliptic operators of the type on the existence of a positive solution for the problem involving critical exponent where Ω is a smooth bounded domain in , , and λ is a real parameter. In particular, we show that if the function has an interior global minimum point x0 such that is comparable to , where and is the identity matrix of order n, then the range of values of λ for which the problem above has a positive solution can change drastically from to . 相似文献
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A. Yu. Savin 《Differential Equations》2011,47(6):897-900
We consider nonlocal operators generated by pseudodifferential operators and the operator of shift along the trajectories
of an arbitrary diffeomorphism of a smooth closed manifold. We introduce the notion of symbol of such operators acting in
Sobolev spaces. As examples, we consider specific diffeomorphisms, namely, isometries and dilations. 相似文献
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We prove Lp-estimates for the Littlewood-Paley function associated with a second order divergence form operator L=–div A with bounded measurable complex coefficients in n.Mathematics Subject Classification (2000):42B20, 35J15The author is partially supported by NSF of China (Grant No. 10371134) and SRF for ROCS, SEM. 相似文献
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V. A. Liskevich 《Ukrainian Mathematical Journal》1989,41(5):615-619
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 710–716, May, 1989. 相似文献
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Victor I. Burenkov 《Journal of Differential Equations》2008,244(7):1712-1740
We prove sharp stability results for the dependence of the eigenvalues of second order uniformly elliptic linear operators with homogeneous Dirichlet boundary conditions upon domain perturbation. 相似文献
8.
Andrea Posilicano 《Mathematische Nachrichten》2014,287(16):1848-1885
Let be bounded with a smooth boundary Γ and let S be the symmetric operator in given by the minimal realization of a second order elliptic differential operator. We give a complete classification of the Markovian self‐adjoint extensions of S by providing an explicit one‐to‐one correspondence between such extensions and the class of Dirichlet forms in which are additively decomposable by the bilinear form of the Dirichlet‐to‐Neumann operator plus a Markovian form. By such a result two further equivalent classifications are provided: the first one is expressed in terms of an additive decomposition of the bilinear forms associated to the extensions, the second one uses the additive decomposition of the resolvents provided by Kre?n's formula. The Markovian part of the decomposition allows to characterize the operator domain of the corresponding extension in terms of Wentzell‐type boundary conditions. Some properties of the extensions, and of the corresponding Dirichlet forms, semigroups and heat kernels, like locality, regularity, irreducibility, recurrence, transience, ultracontractivity and Gaussian bounds are also discussed. 相似文献
9.
Olivier Druet Emmanuel Hebey 《Transactions of the American Mathematical Society》2005,357(5):1915-1929
Let be a smooth compact Riemannian manifold of dimension , and be the Laplace-Beltrami operator. Let also be the critical Sobolev exponent for the embedding of the Sobolev space into Lebesgue's spaces, and be a smooth function on . Elliptic equations of critical Sobolev growth such as
have been the target of investigation for decades. A very nice -theory for the asymptotic behaviour of solutions of such equations has been available since the 1980's. The -theory was recently developed by Druet-Hebey-Robert. Such a theory provides sharp pointwise estimates for the asymptotic behaviour of solutions of . It was used as a key point by Druet to prove compactness results for equations such as . An important issue in the field of blow-up analysis, in particular with respect to previous work by Druet and Druet-Hebey-Robert, is to get explicit nontrivial examples of blowing-up sequences of solutions of . We present such examples in this article.
have been the target of investigation for decades. A very nice -theory for the asymptotic behaviour of solutions of such equations has been available since the 1980's. The -theory was recently developed by Druet-Hebey-Robert. Such a theory provides sharp pointwise estimates for the asymptotic behaviour of solutions of . It was used as a key point by Druet to prove compactness results for equations such as . An important issue in the field of blow-up analysis, in particular with respect to previous work by Druet and Druet-Hebey-Robert, is to get explicit nontrivial examples of blowing-up sequences of solutions of . We present such examples in this article.
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Elvise Berchio Filippo Gazzola 《Journal of Mathematical Analysis and Applications》2006,320(2):718-735
By considering the kernels of the first two traces, four different second order Sobolev spaces may be constructed. For these spaces, embeddings into Lebesgue spaces, the best embedding constant and the possible existence of minimizers are studied. The Euler equation corresponding to some of these minimization problems is a semilinear biharmonic equation with boundary conditions involving third order derivatives: it is shown that the complementing condition is satisfied. 相似文献
15.
Nonlinear partial differential operators having the form G(u) = g(u, D1u,…, DNu), with g?C(R × RN), are here shown to be precisely those operators which are local, (locally) uniformly continuous on, , and (roughly speaking) translation invariant. It is also shown that all such partial differential operators are necessarily bounded and continuous with respect to the norm topologies of . 相似文献
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E. I. Pustylnik 《Integral Equations and Operator Theory》1995,22(4):476-498
The functional calculus of positive operators is applied to second-order elliptic operatorsP. For any absolutely concave (t), the corresponding operators (P
–1) are represented as integral operators, their kernels are estimated, and these estimates are used for studying (P
–1) in Lorentz, Marcinkiewicz and Orlicz spaces. Most of results obtained are sharp. 相似文献
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Murray Cantor 《Journal of Differential Equations》1979,34(1):102-113
In this paper we show the Dirichlet and Neumann problems over exterior regions have unique solutions in certain weighted Sobolev spaces. Two applications are given: (1) The Dirichlet problem for semi-linear operators, and (2) a Helmholtz decomposition for vector fields on exterior regions. 相似文献
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The uniqueness and the non–uniqueness of the Gevrey ultradifferentiable solutions to the Cauchy problem for a class of second order degenerate elliptic operators is studied. Some uniqueness results are proved and the necessity of the hypotheses is discussed by the construction of some counter-examples. 相似文献