Lipschitz

We will also use the theorem on contraction mappings. A mapping S y —> y is called a contraction mapping if it is Lipschitz continuous,... 

Take the norm of both parts of this equality and use the Lipschitz continuity of P (see Lemma 1.2). By the linearity of I, it provides... 

Theorem 1.22. For strongly monotonous and Lipschitz continuous operator A satisfying (1.129), (1.130), there exists a unique solution u G K of the variational inequality (1.126) and... 

Here is the space of functions having k Lipschitz continuous deriva-... 

Extend Sc up to the boundary F such that fl is divided into two domains with Lipschitz boundaries dfli,dfl2- Assume that mens (F n 90 ) > 0, i = 1,2. In each of these domains, for u G the second Korn... 

Proof. Consider a smooth extension of the graph beyond the point X = 1. In so doing we assume that the angle between the boundary L and the extended graph is positive. The domain is divided into two subdomains fli, 0,2 with Lipschitz boundaries cAIi, 80,2. Of course, in the case under consideration the boundaries T, T are different sets. The inclusion (%, G Kq means that the following inequalities are holding true,... 

Let fl C he an open, bounded and connected set with a smooth boundary T, and Tc C R be a smooth orientable two-dimensional surface. We assume that this surface can be extended up to the outer boundary T in such a way that fl is divided into two subdomains Ri, fl2 with Lipschitz boundaries. We assume that this inner surface Tc is described parametrically by the equations... 

Again, let c i be a bounded domain with a smooth boundary T and Tc C H be a smooth orientable two-dimensional surface with a regular boundary. We assume that Tc can be extended in such a way that the domain fl is divided into two parts with Lipschitz boundaries. The surface Tc can be described parametrically... 

Assume that D C is a bounded domain with a Lipschitz boundary 7, and 7o is a curve being a part of 7 such that the length of 70 is positive. Denote by the subspace of the space IFf(D) consisting of all... 

Lipschitz boundaries as in the proof of Theorem 5.5. Then, by Lemma 5.1... 

C. Lipschitz, H. Iith, G. J. de Jong, U. A. Th Brinkman and R. W. Frei, Trace emich-ment of pyrimidine nucleobases, 5-fluoro-uracil and bromacil on a silver-loaded tliiol stationaty phase with on-line reversed-phase high-perfomance liquid cliromatography , J. Chromatogr. 471 321-334 (1989). 

A priori estimates in the case of a variable operator A. So far we have established stability in Ha under the agreement that operator A is constant, that is, independent of t. In the case when A(t) = A t) > 0 depends on t, this obstacle necessitates imposing the Lipschitz continuity of the operator A(t) in the variable t... 

Schemes with variable operators. If operators A and R depend on the variable t, the extra property of the Lipschitz continuity of A and R with respect to the variable t is needed in this connection ... 

Armijo, L. Minimization of Functions Having Lipschitz Continuous First Partial Derivatives. Pac J Math 16 1-3 (1966). 

Pinter, J. D. Global Optimization in Action (Continuous and Lipschitz Optimization Algorithms, Implementations, and Applications). Kluwer Academic Publishers, Norwell, MA (1996a). 

The use of salivary assessments has helped supply data in studies of children and adolescents, for whom even a blood draw may be too invasive, and also helped in our evaluation of longitudinal outcomes. King et al. (2001) observed significantly low cortisol levels in children aged 5-7 years who had been sexually abused compared to control subjects. Goenjian et al. (1996) demonstrated a relationship between low sahvary cortisol levels and PTSD symptoms in adolescents exposed to the Armenian earthquake. However, both lipschitz et al. (2003) and Carrion et al. (2002) failed to note differences in salivary cortisol levels at basehne in multiply traumatized adolescents. 

Lipschitz DS, Rasmusson AM, Yehuda R, Wang S, Anyan W, Gueoguieva R, GrUo CM, Fehon DC, Southwick SM (2003) Salivary cortisol response to dexamethasone in adolescents with posttramnatic stress disorder. J Am Acad Child Adolesc Psychiatry 42 1310-1317... 

Rasmusson AM, Lipschitz DS, Wang S, Hu S, Vojvoda D, Bremner JD, Southwick SM, Charney D (2001) Increased pituitary and adrenal reactivity in premenopausal women with posttramnatic stress disorder. Biol Psychiatry 12 965-977... 

Amaya-Jackson, L.. Newman, E., and Lipschitz, D. (2000) The Child PTSD Checklist. Presented at the Annual Meeting of the American Academy of Child and Adolescent Psychiatry, October 2000. 

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