Direct Methods in the Calculus of Variations

Authors:

ISBN: 978-0-387-35779-9 (Print) 978-0-387-55249-1 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii

  2. Convex analysis and the scalar case

    1. No Access

      Book Chapter

      Pages 1-27

      Introduction

    2. No Access

      Book Chapter

      Pages 31-71

      Convex sets and convex functions

    3. No Access

      Book Chapter

      Pages 73-117

      Lower semicontinuity and existence theorems

    4. No Access

      Book Chapter

      Pages 119-151

      The one dimensional case

  3. Quasiconvex analysis and the vectorial case

    1. No Access

      Book Chapter

      Pages 155-263

      Polyconvex, quasiconvex and rank one convex functions

    2. No Access

      Book Chapter

      Pages 265-312

      Polyconvex, quasiconvex and rank one convex envelopes

    3. No Access

      Book Chapter

      Pages 313-366

      Polyconvex, quasiconvex and rank one convex sets

    4. No Access

      Book Chapter

      Pages 367-411

      Lower semi continuity and existence theorems in the vectorial case

  4. Relaxation and non-convex problems

    1. No Access

      Book Chapter

      Pages 415-437

      Relaxation theorems

    2. No Access

      Book Chapter

      Pages 439-463

      Implicit partial differential equations

    3. No Access

      Book Chapter

      Pages 465-499

      Existence of minima for non-quasiconvex integrands

  5. Miscellaneous

    1. No Access

      Book Chapter

      Pages 503-513

      Function spaces

    2. No Access

      Book Chapter

      Pages 515-527

      Singular values

    3. No Access

      Book Chapter

      Pages 529-547

      Some underdetermined partial differential equations

    4. No Access

      Book Chapter

      Pages 549-567

      Extension of Lipschitz functions on Banach spaces

  6. Back Matter

    Pages 569-621