Journal of Convex Analysis 28 (2021), No. 2, 329--352
Copyright Heldermann Verlag 2021
Existence Issues for a Large Class of Degenerate Elliptic Equations with Nonlinear Hamiltonians
Isabeau Birindelli
Dip. di Matematica Guido Castelnuovo, Sapienza Universitŕ di Roma, Italy
isabeau@mat.uniroma1.it
Giulio Galise
Dip. di Matematica Guido Castelnuovo, Sapienza Universitŕ di Roma, Italy
galise@mat.uniroma1.it
Andrei Rodríguez-Paredes
Dep. de Matemática y Ciencia de la Computación, Universidad de Santiago, Chile
andrei.rodriguez@usach.cl
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-Ampčre operator.
Keywords: Degenerate elliptic equations, viscosity solutions, uniformly convex domains.
MSC: 35B51, 35D40, 35J25, 35J70, 35J96.
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