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Zeitschrift für Analysis und ihre Anwendungen


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Volume 13, Issue 2, 1994, pp. 199–207
DOI: 10.4171/ZAA/515

Published online: 1994-06-30

Perron’s Method and Barrier Functions for the Viscosity Solutions of the Dirichlet Problem for some Non-Linear Partial Differential Equations

M. Ramaswamy[1] and S. Ramaswamy[2]

(1) Indian Institute of Science, Bangalore, India
(2) Indian Institute of Science, Bangalore, India

The Dirichlet problem for some non-linear partial differential equations via Perron’s method is studied in the viscosity set up, by considering two families of functions, instead of one, as considered by others before. The notion of barrier at a boundary point is introduced to study the regularity of boundary points. Barriers for some non-linear operators are also constructed.

Keywords: Viscosity super- and subsolutions, Perron families, resolutive functions, barriers

Ramaswamy M., Ramaswamy S.: Perron’s Method and Barrier Functions for the Viscosity Solutions of the Dirichlet Problem for some Non-Linear Partial Differential Equations. Z. Anal. Anwend. 13 (1994), 199-207. doi: 10.4171/ZAA/515