Jindrich Necas, Professor Emeritus of the Charles University in Prague, Distinguished Researcher Professor at the University of Northern Illinois, DeKalb, Doctor Honoris Causa at the Technical University of Dresden, a leading Czech mathematician and a world-class researcher in the field of partial differential equations. Author or coauthor of 12 monographs, 7 textbooks, and 185 research papers. High points of his research include his contribution to boundary regularity theory for linear systems his contributions to regularity theory of variational integrals, such as his 1977 solution of a long-standing question directly to Hilbert’s 19th problemhis contributions to mathematical theory of the Navier-stokes equations, including his 1995 solution of an important problem raised in a classical 1934 paper by J. Leray.In 1998 he was awarded the Order of Merit of the Czech Republic by President Václav Havel.

From the reviews: "The book includes many important results published as well as unpublished by several authors and results by J. Necas himself. In addition, there are numerous bibliographical hints and many remarks, examples, exercises and problems. ... the book continues to be one of the classics of the Sobolev space setting of linear elliptic boundary value problems. ... the now available English translation will be widely used by young researchers." (Joachim Naumann, Zentralblatt MATH, Vol. 1246, 2012)

• 1.Introduction to the problem.- 2.Sobolev spaces.- 3.Exitence, Uniqueness of basic problems.- 4.Regularity of solution.- 5.Applications of Rellich’s inequalities and generalization to boundary value problems.- 6.Sobolev spaces with weights and applications to the boundary value problems.- 7.Regularity of solutions in case of irregular domains and elliptic problems with variable coefficients.

Jindrich Necas, Professor Emeritus of the Charles University in Prague, Distinguished Researcher Professor at the University of Northern Illinois, DeKalb, Doctor Honoris Causa at the Technical University of Dresden, a leading Czech mathematician and a world-class researcher in the field of partial differential equations. Author or coauthor of 12 monographs, 7 textbooks, and 185 research papers. High points of his research include his contribution to boundary regularity theory for linear systems his contributions to regularity theory of variational integrals, such as his 1977 solution of a long-standing question directly to Hilbert’s 19th problemhis contributions to mathematical theory of the Navier-stokes equations, including his 1995 solution of an important problem raised in a classical 1934 paper by J. Leray.In 1998 he was awarded the Order of Merit of the Czech Republic by President Václav Havel.

From the reviews: "The book includes many important results published as well as unpublished by several authors and results by J. Necas himself. In addition, there are numerous bibliographical hints and many remarks, examples, exercises and problems. ... the book continues to be one of the classics of the Sobolev space setting of linear elliptic boundary value problems. ... the now available English translation will be widely used by young researchers." (Joachim Naumann, Zentralblatt MATH, Vol. 1246, 2012)

• 1.Introduction to the problem.- 2.Sobolev spaces.- 3.Exitence, Uniqueness of basic problems.- 4.Regularity of solution.- 5.Applications of Rellich’s inequalities and generalization to boundary value problems.- 6.Sobolev spaces with weights and applications to the boundary value problems.- 7.Regularity of solutions in case of irregular domains and elliptic problems with variable coefficients.

Jindrich Necas, Professor Emeritus of the Charles University in Prague, Distinguished Researcher Professor at the University of Northern Illinois, DeKalb, Doctor Honoris Causa at the Technical University of Dresden, a leading Czech mathematician and a world-class researcher in the field of partial differential equations. Author or coauthor of 12 monographs, 7 textbooks, and 185 research papers. High points of his research include his contribution to boundary regularity theory for linear systems his contributions to regularity theory of variational integrals, such as his 1977 solution of a long-standing question directly to Hilbert’s 19th problemhis contributions to mathematical theory of the Navier-stokes equations, including his 1995 solution of an important problem raised in a classical 1934 paper by J. Leray.In 1998 he was awarded the Order of Merit of the Czech Republic by President Václav Havel.

From the reviews: "The book includes many important results published as well as unpublished by several authors and results by J. Necas himself. In addition, there are numerous bibliographical hints and many remarks, examples, exercises and problems. ... the book continues to be one of the classics of the Sobolev space setting of linear elliptic boundary value problems. ... the now available English translation will be widely used by young researchers." (Joachim Naumann, Zentralblatt MATH, Vol. 1246, 2012)

• 1.Introduction to the problem.- 2.Sobolev spaces.- 3.Exitence, Uniqueness of basic problems.- 4.Regularity of solution.- 5.Applications of Rellich’s inequalities and generalization to boundary value problems.- 6.Sobolev spaces with weights and applications to the boundary value problems.- 7.Regularity of solutions in case of irregular domains and elliptic problems with variable coefficients.