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  • 1.
    Aronsson, Gunnar
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Crandall, M.G.
    Department of Mathematics, Univ. of California, Santa Barbara, Santa Barbara, CA 93106.
    Juutinen, P.
    Department of Mathematics, P.O. Box 35, FIN-40014 Jyväskylä, Finland.
    A tour of the theory of absolutely minimizing functions2004In: Bulletin of the American Mathematical Society, ISSN 0273-0979, E-ISSN 1088-9485, Vol. 41, no 4, p. 439-505Article in journal (Refereed)
    Abstract [en]

    These notes are intended to be a rather complete and self-contained exposition of the theory of absolutely minimizing Lipschitz extensions, presented in detail and in a form accessible to readers without any prior knowledge of the subject. In particular, we improve known results regarding existence via arguments that are simpler than those that can be found in the literature. We present a proof of the main known uniqueness result which is largely self-contained and does not rely on the theory of viscosity solutions. A unifying idea in our approach is the use of cone functions. This elementary geometric device renders the theory versatile and transparent. A number of tools and issues routinely encountered in the theory of elliptic partial differential equations are illustrated here in an especially clean manner, free from burdensome technicalities - indeed, usually free from partial differential equations themselves. These include a priori continuity estimates, the Harnack inequality, Perron's method for proving existence results, uniqueness and regularity questions, and some basic tools of viscosity solution theory. We believe that our presentation provides a unified summary of the existing theory as well as new results of interest to experts and researchers and, at the same time, a source which can be used for introducing students to some significant analytical tools.

  • 2.
    Aronsson, Gunnar
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Crandall, Michael
    Mathematics University of California.
    Juutinen, Petri
    Mathematics University of Jyväskylä.
    A TOUR OF THE THEORY OF ABSOLUTELY MINIMIZING FUNCTIONS2004In: Bulletin of the American Mathematical Society, ISSN 0273-0979, E-ISSN 1088-9485, Vol. 41, no 4, p. 439-505Article in journal (Refereed)
    Abstract [en]

    A detailed analysis of the class of absolutely minimizing functions in Euclidean spaces and the relationship to the infinity Laplace equation

1 - 2 of 2
CiteExportLink to result list
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  • harvard1
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