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A Visit with the ∞-Laplace Equation

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Calculus of Variations and Nonlinear Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1927))

In these notes we present an outline of the theory of the archetypal L∞ variational problem in the calculus of variations. Namely, given an open U ⊂ IRn and b ∈ C(∂U), find u ∈ C (Ū) which agrees with the boundary function b on ∂U and minimizes

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA

    Michael G. Crandall

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  1. Michael G. Crandall
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Editors and Affiliations

  1. Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 8, 1015, Lausanne, Switzerland

    Bernard Dacorogna

  2. Dipartimento di Matematica, Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Paolo Marcellini

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Crandall, M.G. (2008). A Visit with the ∞-Laplace Equation. In: Dacorogna, B., Marcellini, P. (eds) Calculus of Variations and Nonlinear Partial Differential Equations. Lecture Notes in Mathematics, vol 1927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75914-0_3

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