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¸ cËœ oes Fundamentais da Universidade Lisboaâ€, in collaboration with the “Centro de Matem´ atica da Universidade de Coimbraâ€, the “Centro de Matem´ atica Aplicada do IST/Universidade T´ ecnica de Lisboaâ€, the “Centro de Matem´ atica da Universidade da Beira Interiorâ€,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.