Existence of smooth solutions of problems for parabolic systems with convex constraints on the boundary of the domain

The existence of a smooth solution for problems with a convex constraint on the boundary is proved. The parabolic operator has a diagonal form and a quadratic growth with respect to the gradient. The obtained solution has the maximal possible regularity for problems with boundary obstacles.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 171, pp. 5–11, 1989.     

Palladium nanoparticles stabilized by sterically hindered phosphonium salts as Suzuki cross-coupling catalysts

Palladium nanoparticles with an average size of 2.5±0.5 nm formed from palladium acetate in the presence of tri-tert-butyl(decyl)phosphonium tetrafluoroborate without an additional reducing agent exhibit high activity as a catalyst for the Suzuki cross-coupling reaction involving bromo- and chloroarenes under mild conditions.     

Complexes based on citrus pectin for delivery of tetracycline

The formation of complexes of sodium polygalacturonate with the antimicrobial drug tetracycline was confirmed by UV spectroscopy, powder X-ray diffraction, and dynamic light scattering. The stoichiometry of the complexes with the maximum tetracycline content (6.68 wt.%) was determined. The morphological characteristics of the synthesized complexes were studied by scanning electron microscopy in comparison with the initial compounds.

     

Micellar nanocontainers based on sterically hindered cationic phosphonium amphiphiles

Russian Chemical Bulletin - Self-aggregation processes in an H2O—DMF (10%) medium were studied for a homologous series of tri-tert-butyl(n-alkyl)phosphonium tetrafluoroborates (PIL-n, where n...     

Modifications of the Gehring lemma appearing in the study of parabolic initial-boundary-value problems

Some modifications of the Gehring lemma are required in the study of solutions to parabolic initialboundary-value problems, The Gehring lemma assert that if a function satisfies the reverse Hölder inequalitites in a cube, then the integrability degree of this function in Q increases in this cube. Earlier, the author formulated some generalizations of the Gehring lemma and used them in the study of parabolic quasilinear systems with controlled nonlinearity orders. In this paper, the proof of these generalizations are given. On the basis of the modification of the Gehring lemma proposed by the author, the theorem on the reverse Hölder inequalities is formulated in a form convenient for obtaining L^p-estimates for the derivatives of solutions to parabolic problems. An application of this theorem is also demonstrated. Bibliography: 19 titles.     

Limiting smoothness of the solution of a nonstationary problem with one or two obstacles

The regularity of the solution of a nonstationary problem with an obstable for various forms of parabolic operators has been thoroughly investigated. Under the condition of sufficient smoothness of the data of the problem, one proves that the solutionW _q ^2,1 (Q) belongs to the Sobolev space In the present paper one establishes that the limiting possible smoothness of the solution of a nonstationary problem with one or two obstacles is the boundedness of the second derivatives of the solution with respect to the spatial variables and of the first derivatives with respect to t. One assumes that the operator is linear and the functions defining the obstacles have the minimal possible smoothness.Translated from Problemy Matematicheskogo Analiza, No. 9, pp. 149–157, 1984.     

The monotonicity condition and a priori estimates of the Hölder norm for a class of nondiagonal elliptic systems with quadratic nonlinearity

The Dirichlet problem for quasilinear elliptic systems of equations with nondiagonal principal matrix and additional terms with strong nonlinearity in the gradient is considered. An a priori condition on the behavior of solutions in a neighborhood of a fixed point is stated, which allows us to estimate locally the Hölder norm of a solution in terms of its energy norm. Owing to the monotonicity inequality proved for one class of such systems, the a priori assumption on the behavior of solutions is reduced to an optimal one while estimating the Hölder norm of the solution. Bibliography: 27 titles.     

Sesquiterpene lactones fromArtemisia halophila

Chemistry of Natural Compounds -