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Area Formulas for σ-Harmonic Mappings

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Nonlinear Problems in Mathematical Physics and Related Topics I

Part of the book series: International Mathematical Series ((IMAT,volume 1))

Abstract

The goal of the present paper is two-fold. First, we review some recent progress concerning generalizations of various classical results, such as sufficient conditions to guarantee univalence of harmonic mappings in dimension two, to certain pairs of elliptic partial differential equations with measurable coefficients. Second, we apply these results to prove new area formulas which are valid for a large class of mappings arising as solutions of these pairs of elliptic partial differential equations. Finally, we briefly discuss some applications to homogenized constants in the context of G-closure problems. To Professor Olga A. Ladyzhenskaya with our deep admiration

To Professor Olga A. Ladyzhenskaya with our deep admiration

† The work is partially supported by the MURST (grant no. MM01111258).

†† The work is partially supported by the MURST (grant no. MM02263577).

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Authors
  1. Giovanni Alessandrini
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  2. Vincenzo Nesi
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Editors and Affiliations

  1. St. Petersburg University, St. Petersburg, Russia

    Michael Sh. Birman  & Nina N. Uraltseva  & 

  2. University of Bonn, Bonn, Germany

    Stefan Hildebrandt

  3. Steklov Institute of Mathematics RAS, St. Petersburg, Russia

    Vsevolod A. Solonnikov

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Alessandrini, G., Nesi, V. (2002). Area Formulas for σ-Harmonic Mappings. In: Birman, M.S., Hildebrandt, S., Solonnikov, V.A., Uraltseva, N.N. (eds) Nonlinear Problems in Mathematical Physics and Related Topics I. International Mathematical Series, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0777-2_1

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  • DOI: https://doi.org/10.1007/978-1-4615-0777-2_1

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