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1.
We consider parabolic variational inequalities having the strong formulation
((1))
where for some admissible initial datum, V is a separable Banach space with separable dual is an appropriate monotone operator, and is a convex, lower semicontinuous functional. Well-posedness of (1) follows from an explicit construction of the related semigroup Illustrative applications to free boundary problems and to parabolic problems in Orlicz-Sobolev spaces are given.  相似文献   

2.
On the atomic conditions of lattice-ordered groups   总被引:2,自引:0,他引:2  
We introduce large convex -subgroups to study the structure of the lattice-ordered groups G whose C(G), P(G) and (G) satisfy atomic conditions, where C(G), P(G) and (G) denote respectively the lattice of all convex -subgroups, the lattice of all polar subgroups and the root system of all regular subgroups of G. In particular, we construct a new torsion class defined as the class of -groups G for which all large prime subgroups are maximal. We prove that the class of hyperarchimedean -groups is properly contained within and that any -group within has the property that any chain of prime subgroups has length at most 2.Received October 7, 2003; accepted in final form June 11, 2004.  相似文献   

3.
4.
For a convex body in which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy (number of integer points minus volume) of a linearly dilated copy is estimated from below. On the basis of a recent method of K. Soundararajan [16], an -bound is obtained that improves upon all earlier results of this kind.Dedicated to the memory of Professor Erich LamprechtThis revised electronic version of the Abstract includes the formulas that were missing in the previous electronic version published online in September 2004.  相似文献   

5.
Suppose A generates a strongly continuous linear group on a Banach space X and B is a linear operator on X. It is shown that an extension of generates a strongly continuous semigroup if and only if the family of operators has an appropriate evolution system. This produces simple sufficient conditions for an extension of to generate a strongly continuous semigroup, including
(1)  being m-dissipative and for all x in the domain of B; or
(2)  being m-dissipative and being a commuting family of operators with
dense. This is applied to many differential operators; for at least one class of applications, the semigroup is generated by the closure of and the equivalence between semigroups and evolution systems enables us to construct it explicitly. In all the applications, including the sufficient conditions (1) and (2) above, the semigroup generated by an extension of is given by the Trotter product formula
  相似文献   

6.
We consider Hilbert spaces of analytic functions defined on an open subset of , stable under the operator Mu of multiplication by some function u. Given a subspace of which is nearly invariant under division by u, we provide a factorization linking each element of to elements of on the inverse image under u of a certain complex disc, for which we give a relatively simple formula. By applying these results to and u(z) = z, we obtain interesting results involving a H2-norm control. In particular, we deduce a factorization for the kernel of Toeplitz operators on Dirichlet spaces. Finally, we give a localization for the problem of extraneous zeros.Submitted: January 18, 2003 Revised: December 20, 2003  相似文献   

7.
8.
A singular rank one perturbation of a self-adjoint operator A in a Hilbert space is considered, where and but with the usual A–scale of Hilbert spaces. A modified version of the Aronszajn-Krein formula is given. It has the form where F denotes the regularized Borel transform of the scalar spectral measure of A associated with . Using this formula we develop a variant of the well known Aronszajn–Donoghue spectral theory for a general rank one perturbation of the class.Submitted: March 14, 2002 Revised: December 15, 2002  相似文献   

9.
In this paper, we consider global solutions for the following nonlinear Schrödinger equation in with and We show that no nontrivial solution can decay faster than the solutions of the free Schrödinger equation, provided that u(0) lies in the weighted Sobolev space in the energy space, namely or in according to the different cases.  相似文献   

10.
We examine the operator algebra behind the boundary integral equation method for solving transmission problems. A new type of boundary integral operator, the rotation operator, is introduced, which is more appropriate than operators of double layer type for solving transmission problems for first order elliptic partial differential equations. We give a general invertibility criteria for operators in by defining a Clifford algebra valued Gelfand transform on . The general theory is applied to transmission problems with strongly Lipschitz interfaces for the two classical elliptic operators and . We here use Rellich techniques in a new way to estimate the full complex spectrum of the boundary integral operators. For we use the associated rotation operator to solve the Hilbert boundary value problem and a Riemann type transmission problem. For the Helmholtz equation, we demonstrate how Rellich estimates give an angular spectral estimate on the rotation operator, which with the general spectral mapping properties in translates to a hyperbolic spectral estimate for the double layer potential operator.  相似文献   

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