Bounds for vertical points of solutions of prescribed mean curvature type equations, I

1989 ◽  
Vol 112 (1-2) ◽  
pp. 15-32 ◽  
Author(s):  
F. V. Atkinson ◽  
L. A. Peletier
Keyword(s):  
Mean Curvature ◽  
Asymptotic Estimates ◽  
Radial Solutions ◽  
Prescribed Mean Curvature ◽  
Capillary Type ◽  
Curvature Type

SynopsisConditions are obtained under which radial solutions of generalised capillary-type equations exhibit a first vertical point, together with bounds and asymptotic estimates for these points.

Estimates for vertical points of solutions of prescribed mean curvature type equations II

1992 ◽  
Vol 5 (4) ◽  
pp. 283-310 ◽  
Author(s):  
F.V. Atkinson ◽  
L.A. Peletier ◽  
J. Serrin
Keyword(s):  
Mean Curvature ◽  
Prescribed Mean Curvature ◽  
Curvature Type

Radial Solutions of the Dirichlet Problem for the Prescribed Mean Curvature Equation in a Robertson-Walker Spacetime

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Daniel de la Fuente ◽  
Alfonso Romero ◽  
Pedro J. Torres
Keyword(s):  
Fixed Point ◽  
Mean Curvature ◽  
Existence Result ◽  
Euclidean Ball ◽  
Radial Solutions ◽  
Curvature Equation ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Equation ◽  
Prescribed Mean Curvature Equation ◽  
Curvature Problem

AbstractWe consider the prescribed mean curvature problem of spacelike graphs in Robertson- Walker spacetimes of flat fiber with homogeneous Dirichlet conditions on an Euclidean ball. Under reasonable assumptions, it is shown that every possible solution must be radially symmetric. Besides, an existence result for a singular nonlinear equation is proved by making use of the classical Schauder fixed point Theorem. The results are applied to realistic examples of Robertson-Walker spacetimes.

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

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