On the growth of supersolutions of nonlinear PDE’s on exterior domains
Copyright policy )On the growth of supersolutions of nonlinear PDE’s on exterior domains
The authors obtain a comparison principle on annuli, with ``catenoid-like'' functions, for supersolutions of non-linear elliptic PDEs \[ L_\phi(u)=\mathrm{div} (|\nabla u|^{-1}\phi(|\nabla u|)\nabla u)\leq 0\leq L_\phi(v_1) \] over exterior domains in a non-positively curved manifold with a pole. This result is applied to get an upper estimate on the growth of such supersolutions and, in particular, of exterior graphs of non-negative mean curvature.
- University of Insubria Italy
- Polytechnic University of Turin Italy
- Università dell Insubria (Varese) Italy
- University of Milano-Bicocca Italy
- University of Milan Italy
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), annuli, nonlinear elliptic operators, Comparison principles in context of PDEs, mean curvature, comparison principle, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, exterior graphs, Nonlinear elliptic equations, growth estimate, supersolutions, Exterior graphs; Growth estimate; Mean curvature; Nonlinear elliptic operators;, Exterior graphs; Growth estimate; Mean curvature; Nonlinear elliptic operators, Exterior graphs; Growth estimate; Mean curvature; Nonlinear elliptic operators; Analysis; Applied Mathematics
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), annuli, nonlinear elliptic operators, Comparison principles in context of PDEs, mean curvature, comparison principle, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, exterior graphs, Nonlinear elliptic equations, growth estimate, supersolutions, Exterior graphs; Growth estimate; Mean curvature; Nonlinear elliptic operators;, Exterior graphs; Growth estimate; Mean curvature; Nonlinear elliptic operators, Exterior graphs; Growth estimate; Mean curvature; Nonlinear elliptic operators; Analysis; Applied Mathematics
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