Nonlinear problems in mathematical physics and related topics I : in honor of Professor O.A. Ladyzhenskaya / edited by Michael Sh. Birman [and others].

Includes bibliographical references and indexes.

Area Formulas for [sigma]-Harmonic Mappings / Giovanni Alessandrini, Vincenzo Nesi 1 -- On a Variational Problem Connected with Phase Transitions of Means in Controllable Dynamical Systems / Vladimir I. Arnold 23 -- A Priori Estimates for Starshaped Compact Hypersurfaces with Prescribed mth Curvature Function in Space Forms / J. Lucas M. Barbosa, Jorge H.S. Lira, Vladimir I. Oliker 35 -- Elliptic Variational Problems with Nonstandard Growth / Michael Bildhauer, Martin Fuchs 53 -- Existence and Regularity of Solutions of d[omega] = f with Dirichlet Boundary Conditions / Bernard Dacorogna 67 -- A Singular Perturbation Property of Capillary Surfaces / Robert Finn 83 -- On Solutions with Fast Decay of Nonstationary Navier-Stokes System in the Half-Space / Yoshiko Fujigaki, Tetsuro Miyakawa 91 -- Strong Solutions to the Problem of Motion of a Rigid Body in a Navier-Stokes Liquid under the Action of Prescribed Forces and Torques / Giovanni P. Galdi, Ana L. Silvestre 121 -- The Partially Free Boundary Problem for Parametric Double Integrals / Stefan Hildebrandt, Heiko von der Mosel 145 -- On Evolution Laws Forcing Convex Surfaces to Shrink to a Point / Nina M. Ivochkina 167 -- Existence of a Generalized Green Function for Integro-Differential Operators of Fractional Order / Moritz Kassmann, Mark Steinhauer 187 -- L[subscript q]-Estimates of the First-Order Derivatives of Solutions to the Nonstationary Stokes Problem / Herbert Koch, Vsevolod A. Solonnikov 203 -- Two Sufficient Conditions for the Regularity of Lateral Boundary for the Heat Equation / Nicolai V. Krylov 219 -- Bound State Asymptotics for Elliptic Operators with Strongly Degenerated Symbols / Ari Laptev, Oleg Safronov, Timo Weidl 233 -- Nonlocal Problems for Quasilinear Parabolic Equations / Gary M. Lieberman 247 -- Boundary Feedback Stabilization of a Vibrating String with an Interior Point Mass / Walter Littman, Stephen W. Taylor 271 -- On Direct Lyapunov Method in Continuum Theories / Mariarosaria Padula 289 -- The Fourier Coefficients of Stokes' Waves / Pavel I. Plotnikov, John F. Toland 303 -- A Geometric Regularity Estimate via Fully Nonlinear Elliptic Equations / Reiner Schatzle 317 -- On the Eigenvalue Estimates for the Weighted Laplacian on Metric Graphs / Michael Solomyak 327 -- Potential Theory for Nonstationary Stokes Problem in Nonconvex Domains / Vsevolod A. Solonnikov 349 -- Stability of Axially Symmetric Solutions to the Navier-Stokes Equations in Cylindrical Domains / Wojciech M. Zajaczkowski 373.

The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday.

O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences.

Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva.

Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role.

Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary.

Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals.