Abstract

Let a:Rn→Rna:\R^n\to\R^n be monotonic, but unnecessarily strictly monotonic. We study the existence of Lipschitz or locally Lipschitz solutions to the equation div a(∇u)=0\,a(\nabla u) = 0 when the Lipschitz boundary datum fulfills some recent unilateral Bounded Slope Conditions.

Author information

Contact details are reproduced from the original publication and may be historical.

Carlo Mariconda

Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy

maricond@math.unipd.it

Keywords

  • Lipschitz
  • nonlinear
  • degenerate
  • elliptic
  • pde
  • convex

Mathematics Subject Classification

35J70, 35J15, 49K20

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Suggested citation

C. Mariconda. “Existence Results for a Non Coercive Homogeneous Nonlinear Elliptic Equation.” Journal of Convex Analysis 19 (2012), No. 3, 795–813. https://doi.org/10.68381/jca19041

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press.