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Analytic semigroups generated in L 1(Ω) by second order elliptic operators via duality methods

Abstract

Given an open domain (possibly unbounded) Ω⊂R n, we prove that uniformly elliptic second order differential operators, under nontangential boundary conditions, generate analytic semigroups in L 1(Ω). We use a duality method, and, further, give estimates of first order derivatives for the resolvent and the semigroup, through properties of the generator in Sobolev spaces of negative order.

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Correspondence to L. Angiuli.

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Communicated by Rainer Nagel.

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Angiuli, L., Pallara, D. & Paronetto, F. Analytic semigroups generated in L 1(Ω) by second order elliptic operators via duality methods. Semigroup Forum 80, 255–271 (2010). https://doi.org/10.1007/s00233-009-9200-y

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Keywords

  • Analytic semigroups
  • General boundary conditions
  • Duality methods