scholarly journals Multiple radial solutions for Dirichlet problem involving two mean curvature equations in Euclidean and Minkowski spaces

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Dirichlet Problem ◽  
Mean Curvature ◽  
Radial Solutions ◽  
Minkowski Spaces ◽  
Mean Curvature Equations

scholarly journals The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz–Minkowski space

2017 ◽  
Vol 24 (1) ◽  
pp. 113-134 ◽  
Author(s):  
Chiara Corsato ◽  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Dirichlet Problem ◽  
Differential Operator ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Differential Operators ◽  
Curvature Equation ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Equation ◽  
Prescribed Mean Curvature Equation ◽  
Mean Curvature Equations

AbstractWe discuss existence, multiplicity, localisation and stability properties of solutions of the Dirichlet problem associated with the gradient dependent prescribed mean curvature equation in the Lorentz–Minkowski space$\left\{\begin{aligned} \displaystyle{-}\operatorname{div}\biggl{(}\frac{\nabla u% }{\sqrt{1-|\nabla u|^{2}}}\biggr{)}&\displaystyle=f(x,u,\nabla u)&&% \displaystyle\phantom{}\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{on }\partial% \Omega.\end{aligned}\right.$The obtained results display various peculiarities, which are due to the special features of the involved differential operator and have no counterpart for elliptic problems driven by other quasilinear differential operators. This research is also motivated by some recent achievements in the study of prescribed mean curvature graphs in certain Friedmann–Lemaître–Robertson–Walker, as well as Schwarzschild–Reissner–Nordström, spacetimes.

Radial solutions for systems involving mean curvature operators in Euclidean and Minkowski spaces

2009 ◽  
Author(s):  
Cristian Bereanu ◽  
Petru Jebelean ◽  
Jean Mawhin ◽  
Alberto Cabada ◽  
Eduardo Liz ◽  
...  
Keyword(s):  
Mean Curvature ◽  
Radial Solutions ◽  
Minkowski Spaces

scholarly journals On the Dirichlet problem of prescribed mean curvature equations without H-convexity condition

2000 ◽  
Vol 157 ◽  
pp. 177-209 ◽  
Author(s):  
Kazuya Hayasida ◽  
Masao Nakatani
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Existence Theorem ◽  
Mean Curvature ◽  
Weak Sense ◽  
Convexity Condition ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Equations ◽  
Well Posed

The Dirichlet problem of prescribed mean curvature equations is well posed, if the boundery is H-convex. In this article we eliminate the H-convexity condition from a portion Γ of the boundary and prove the existence theorem, where the boundary condition is satisfied on Γ in the weak sense.

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