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Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

Plasticity. --- Newtonian fluids. --- Calculus of variations. --- Calcul des variations --- Calculus of variations --- Newtonian fluids --- Plasticiteit --- Plasticity --- Plasticité --- Variatieberekening --- Applied mathematics. --- Engineering mathematics. --- Mechanics. --- Mathematical physics. --- Partial differential equations. --- Applications of Mathematics. --- Classical Mechanics. --- Theoretical, Mathematical and Computational Physics. --- Partial Differential Equations. --- Partial differential equations --- Physical mathematics --- Physics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics

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Partial differential equations --- Mathematical physics --- Gases handling. Fluids handling --- differentiaalvergelijkingen --- wiskunde --- fysica --- vloeistoffen

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Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathema- ciansfromtheSt.PetersburgMathematicalSchool.Hisremarkableresultsonexact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, and Stokes systems, his methods and contributions to the - vestigation of free boundary problems, in particular in ?uid mechanics, are well known to specialists all over the world. The International Conference on Trends in Partial Di?erential Equations of th ´ Mathematical Physics  was held on the occasion of his 70 birthday in Obidos (Portugal), from June 7 to 10, 2003. It was an organization of the Centro de Matem´ atica e Aplica¸ c˜ oes Fundamentais da Universidade Lisboa , in collaboration with the Centro de Matem´ atica da Universidade de Coimbra , the Centro de Matem´ atica Aplicada do IST/Universidade T´ ecnica de Lisboa , the Centro de Matem´ atica da Universidade da Beira Interior ,from Portugal,and with the L- oratory of Mathematical Physics of the St.Petersburg Department of the Steklov Institute of Mathematics from Russia. The conference consisted of thirty eight invited and contributed lectures and ´ gathered,inthecharminganduniquemedievaltownofObidos,aboutsixtypart- ipants from ?fteen countries, namely USA, Switzerland, Spain, Russia, Portugal, Poland, Lithuania, Korea, Japan, Italy, Germany, France, Canada, Australia and Argentina.Severalcolleaguesgaveusahelpinghandintheorganizationofthec- ference. We are thankful to all of them, and in particular to Stanislav Antontsev, Anvarbek Meirmanov and Ad´ elia Sequeira, that integrated also the Organizing Committee. A special acknowledgement is due to Elena Frolova that helped us in compiling the short and necessarily incomplete bio-bibliographical notes below.

Partial differential equations --- Mathematical physics --- Gases handling. Fluids handling --- differentiaalvergelijkingen --- wiskunde --- fysica --- vloeistoffen

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This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.

Differential equations, Partial --- Mathematical physics --- Differential equations, partial. --- Mathematical physics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Fluid- and Aerodynamics. --- Physical mathematics --- Physics --- Partial differential equations --- Mathematics --- Partial differential equations. --- Physics. --- Fluids. --- Hydraulics --- Mechanics --- Hydrostatics --- Permeability --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics