简介
Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St. Petersburg Mathematical School. His remarkable results on exact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, Stokes and Navier-Stokes systems, his methods and contributions to the inverstigation of free boundary problems, in particular in fluid mechanics, are well known to specialists all over the world. The International Conference on "Trends in Partial Differential Equations of Mathematical Physics" was held on the occasion of his 70th birthday in A"bidos (Portugal) from June 7 to 10, 2003. The conference consisted of thirty-eight invited and contributed lectures and gathered, in the charming and unique medieval town of A"bidos, about sixty participants from fifteen countries. This book contains twenty original contributions on many topics related to V.A. Solonnikov's work, selected from the invited talks of the conference.
目录
Front matter 1-14
Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing 15-26
Ultracontractive Bounds for Nonlinear Evolution Equations Governed by the Subcritical p-Laplacian 27-35
Weighted L2-spaces and Strong Solutions of the Navier-Stokes Equations in
37-44
A Limit Model for Unidirectional Non-Newtonian Flows with Nonlocal Viscosity 45-64
On the Problem of Thermocapillary Convection for Two Incompressible Fluids Separated by a Closed Interface 65-80
Some Mathematical Problems in Visual Transduction 81-89
Global Regularity in Sobolev Spaces for Elliptic Problems with p-structure on Bounded Domains 91-108
Temperature Driven Mass Transport in Concentrated Saturated Solutions 109-124
Solvability of a Free Boundary Problem for the Navier-Stokes Equations Describing the Motion of Viscous Incompressible Nonhomogeneous Fluid 125-136
Duality Principles for Fully Nonlinear Elliptic Equations 137-148
On the B茅nard Problem 149-160
Exact Boundary Controllability for Quasilinear Wave Equations 161-185
Regularity of Euler Equations for a Class of Three-Dimensional Initial Data 187-195
A Model of a Two-dimensional Pump 197-212
Regularity of a Weak Solution to the Navier-Stokes Equation in Dependence on Eigenvalues and Eigenvectors of the Rate of Deformation Tensor 213-223
Free Work and Control of Equilibrium Configurations 225-241
Stochastic Geometry Approach to the Kinematic Dynamo Equation of Magnetohydrodynamics 243-256
Quasi-Lipschitz Conditions in Euler Flows 257-273
Interfaces in Solutions of Diffusion-absorption Equations in Arbitrary Space Dimension 275-282
Estimates for Solutions of Fully Nonlinear Discrete Schemes Estimates for Solutions of Fully Nonlinear Discrete Schemes
Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing 15-26
Ultracontractive Bounds for Nonlinear Evolution Equations Governed by the Subcritical p-Laplacian 27-35
Weighted L2-spaces and Strong Solutions of the Navier-Stokes Equations in
37-44
A Limit Model for Unidirectional Non-Newtonian Flows with Nonlocal Viscosity 45-64
On the Problem of Thermocapillary Convection for Two Incompressible Fluids Separated by a Closed Interface 65-80
Some Mathematical Problems in Visual Transduction 81-89
Global Regularity in Sobolev Spaces for Elliptic Problems with p-structure on Bounded Domains 91-108
Temperature Driven Mass Transport in Concentrated Saturated Solutions 109-124
Solvability of a Free Boundary Problem for the Navier-Stokes Equations Describing the Motion of Viscous Incompressible Nonhomogeneous Fluid 125-136
Duality Principles for Fully Nonlinear Elliptic Equations 137-148
On the B茅nard Problem 149-160
Exact Boundary Controllability for Quasilinear Wave Equations 161-185
Regularity of Euler Equations for a Class of Three-Dimensional Initial Data 187-195
A Model of a Two-dimensional Pump 197-212
Regularity of a Weak Solution to the Navier-Stokes Equation in Dependence on Eigenvalues and Eigenvectors of the Rate of Deformation Tensor 213-223
Free Work and Control of Equilibrium Configurations 225-241
Stochastic Geometry Approach to the Kinematic Dynamo Equation of Magnetohydrodynamics 243-256
Quasi-Lipschitz Conditions in Euler Flows 257-273
Interfaces in Solutions of Diffusion-absorption Equations in Arbitrary Space Dimension 275-282
Estimates for Solutions of Fully Nonlinear Discrete Schemes Estimates for Solutions of Fully Nonlinear Discrete Schemes
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