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Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames

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Abstract

The main result of this paper is a general Hölder estimate in a class of singularly perturbed elliptic systems. This estimate is applied to the study of the well-known Burke–Schuman approximation in flame theory. After reviewing some classical cases (equidiffusional case; high activation energy approximation) we turn to the non-equidiffusional case, and to nonlinear diffusion models. The limiting problems are nonlinear elliptic equations; they have Hölder or Lipschitz maximal global regularity. A natural question is then whether this regularity is kept uniformly throughout the approximation process, and we show that this is true in general.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712-1082, USA

    Luis A. Caffarelli

  2. UMR CNRS 5640 and Institut Universitaire de France, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex, France

    Jean-Michel Roquejoffre

Authors
  1. Luis A. Caffarelli
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  2. Jean-Michel Roquejoffre
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Correspondence to Jean-Michel Roquejoffre.

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Communicated by Y. Brenier

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Caffarelli, L.A., Roquejoffre, JM. Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames. Arch Rational Mech Anal 183, 457–487 (2007). https://doi.org/10.1007/s00205-006-0013-9

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  • DOI: https://doi.org/10.1007/s00205-006-0013-9

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