Front-Tracking and Variational Methods to Approximate Interfaces with Prescribed Mean Curvature

1991 ◽  
pp. 83-92 ◽  
Author(s):  
G. Bellettini ◽  
M. Paolini ◽  
C. Verdi
Keyword(s):  
Variational Methods ◽  
Mean Curvature ◽  
Front Tracking ◽  
Prescribed Mean Curvature

A VARIATIONAL APPROACH FOR ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE PROBLEMS

2014 ◽  
Vol 97 (2) ◽  
pp. 145-161 ◽  
Author(s):  
GHASEM A. AFROUZI ◽  
ARMIN HADJIAN ◽  
GIOVANNI MOLICA BISCI
Keyword(s):  
Variational Methods ◽  
Mean Curvature ◽  
Variational Approach ◽  
Regularity Result ◽  
Nontrivial Solutions ◽  
One Dimensional ◽  
Prescribed Mean Curvature ◽  
Nonnegative Solutions ◽  
Curvature Problem

AbstractWe discuss the multiplicity of nonnegative solutions of a parametric one-dimensional mean curvature problem. Our main effort here is to describe the configuration of the limits of a certain function, depending on the potential at zero, that yield, for certain values of the parameter, the existence of infinitely many weak nonnegative and nontrivial solutions. Moreover, thanks to a classical regularity result due to Lieberman, this sequence of solutions strongly converges to zero in $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}C^1([0,1])$. Our approach is based on recent variational methods.

Positive Solutions of an Indefinite Prescribed Mean Curvature Problem on a General Domain

2004 ◽  
Vol 4 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Patrick Habets ◽  
Pierpaolo Omari
Keyword(s):  
Positive Solutions ◽  
Mean Curvature ◽  
General Domain ◽  
Prescribed Mean Curvature ◽  
Existence Of Positive Solutions ◽  
Curvature Problem

AbstractThe existence of positive solutions is proved for the prescribed mean curvature problemwhere Ω ⊂ℝ

scholarly journals Embedded tori with prescribed mean curvature

2018 ◽  
Vol 340 ◽  
pp. 406-458 ◽  
Author(s):  
Paolo Caldiroli ◽  
Monica Musso
Keyword(s):  
Mean Curvature ◽  
Prescribed Mean Curvature
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