Abstract

For degenerate elliptic equations with a nonlinear gradient term H, in bounded uniformly convex domains Ω, we give sufficient conditions for the existence and uniqueness of solutions in terms of the size of Ω, of the forcing term f and of H. The results apply to a wide class of equations, having as principal part significant examples, e.g. linear degenerate operators, weighted partial trace operators and the homogeneous Monge-Ampère operator.

Author information

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

Andrei Rodríguez-Paredes

Dep. de Matemática y Ciencia de la Computación, Universidad de Santiago, Chile

andrei.rodriguez@usach.cl

Keywords

  • Degenerate elliptic equations
  • viscosity solutions
  • uniformly convex domains

Mathematics Subject Classification

35B51, 35D40, 35J25, 35J70, 35J96

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Suggested citation

I. Birindelli, G. Galise, A. Rodríguez-Paredes. “Existence Issues for a Large Class of Degenerate Elliptic Equations with Nonlinear Hamiltonians.” Journal of Convex Analysis 28 (2021), No. 2, 329–352. https://doi.org/10.68381/jca28021

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.