Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 77)


For Schrödinger operators, the inclusion of a magnetic field raises the energy. This is the consequence of a basic inequality due to Kato. A variation on this question—namely, monotonicity of the ground state energy as a function of the parameter B—is of central importance in the theory of superconductivity and is discussed in Section 2.3 here and repeatedly in the book.


Ground State Energy Multivalued Function Harnack Inequality Magnetic Potential Basic Inequality 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAarhus UniversityAarhus CDenmark
  2. 2.Département de MathématiquesUniversité Paris-Sud and CNRSOrsay CedexFrance

Personalised recommendations