Some Relative Isoperimetric Inequalities and Applications to Nonlinear Problems

  • Filomena Pacella
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)


The importance of isoperimetric inequalities in many problems in Analysis as well as in Differential Geometry or in Mathematical Phisics is well known. ([3], [11], [22], [25], [4], [12]). In particular the classical isoperimetric inequality, which states that among all sets of fixed finite measure the ball has the smallest perimeter (in the sense of De Giorgi [8]), plays a fondamental role in the symmetrization of Dirichlet problems ([3], [27], [28]), in studying Sobolev inequalities ([22], [26]) and, more generally, in deriving geometrical properties for solutions of partial differential equations ([16], [19], [25]).


Dirichlet Problem Convex Cone Sobolev Inequality Mixed Boundary Isoperimetric Inequality 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Filomena Pacella
    • 1
  1. 1.Dipartimento di MatematicaUniversitá di Roma I “La Sapienza”RomaItaly

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