Geodesic
Growth rate and existence of solutions to Dirichlet problems for prescribed mean curvature equations on unbounded domains
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove growth rate estimates and existence of solutions to Dirichlet problems for prescribed mean curvature equation on unbounded domains inside the complement of a cone or a parabola like region in $\mathbb{R}^n (n\geq 2)$. The existence results are proved using a modified Perron's method by which a subsolution is a solution to the minimal surface equation, while the role played by a supersolution is replaced by estimates on the uniform $C^{0}$ bounds on the liftings of subfunctions on compact sets.
Classification : 35J25, 35J60, 35J65
Keywords: elliptic boundary-value problem, quasilinear elliptic equation, prescribed mean curvature equation, unbounded domain, Perron's method 
@article{EJDE_2008__2008__a8,
     author = {Jin, Zhiren},
     title = {Growth rate and existence of solutions to {Dirichlet} problems for prescribed mean curvature equations on unbounded domains},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a8/}
}
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Jin, Zhiren. Growth rate and existence of solutions to Dirichlet problems for prescribed mean curvature equations on unbounded domains. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a8/