Viscosity solutions on Grushin-type planes
Bieske, Thomas
Illinois J. Math., Tome 46 (2002) no. 3, p. 893-911 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
This paper examines viscosity solutions to a class of fully nonlinear equations on Grushin-type planes. First, viscosity solutions are defined, using subelliptic second order superjets and subjets. Then, a Grushin maximum principle is proved, and as an application, comparison principles for certain types of nonlinear functions follow. This is accomplished by establishing a natural relationship between Euclidean and subelliptic jets, in order to use the viscosity solution technology of Crandall, Ishii, and Lions (1992). The particular example of infinite harmonic functions on certain Grushin-type planes is examined in further detail.
Publié le : 2002-07-15
Classification:  35H20,  35B05,  49L25 
@article{1258130991,
     author = {Bieske, Thomas},
     title = {Viscosity solutions on Grushin-type planes},
     journal = {Illinois J. Math.},
     volume = {46},
     number = {3},
     year = {2002},
     pages = { 893-911},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258130991}
}

Bieske, Thomas. Viscosity solutions on Grushin-type planes. Illinois J. Math., Tome 46 (2002) no. 3, pp.  893-911. http://gdmltest.u-ga.fr/item/1258130991/