• Igor Chueshov
  • Irena Lasiecka
Part of the Springer Monographs in Mathematics book series (SMM)


This chapter collects several preliminary results pertaining to the theory of function spaces and general theory of nonlinear operators. Properties of the biharmonic operator endowed with various boundary conditions (clamped, hinged, free, and mixed) are discussed and the structure and properties of the von Karman bracket, representing the main nonlinearity in von Karman evolutions, are analyzed. The chapter concludes with application of the results mentioned above to stationary (time-independent) von Karman equations.


Banach Space Weak Solution Hardy Space Besov Space Fredholm Operator 
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© Springer Science+Business Media 2010

Authors and Affiliations

  1. 1.Department of Mechanics & MathematicsKharkov National UniversityKharkovUkraine
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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