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The Dirichlet problem for an elliptic equation in an angle with leading homogeneous measurable coefficients

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Summary

In this paper we prove an existence—uniqueness theorem in the context of Sobolev spacesW 2,pα), Θα being an angle of width α, for the Dirichlet problem connected with a second-order elliptic equation, whose leading coefficients are homogeneous bounded measurable functions. Moreover we determine explicitly a neighbourhood I of p=2 depending only on the ratio of the ellipticity constants such that, when p ∈ I, our problem is unconditionally solvable.

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Entrata in Redazione il 7 settembre 1976.

Lavoro eseguito nell'ambito del Gruppo Nazionale di Analisi Funzionale ed Applicazioni del Consiglio Nazionale delle Ricerche.

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Lorenzi, A. The Dirichlet problem for an elliptic equation in an angle with leading homogeneous measurable coefficients. Annali di Matematica 115, 41–97 (1977) doi:10.1007/BF02414711

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Keywords

  • Measurable Function
  • Elliptic Equation
  • Dirichlet Problem
  • Uniqueness Theorem
  • Measurable Coefficient