# Generalized Cheeger sets related to landslides

## Related Articles

- Gross Laplacian Acting on Operators. Horrigue, Samah; Ouerdiane, Habib // Acta Applicandae Mathematica;Feb2009, Vol. 105 Issue 2, p227
In this paper, we introduce a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian, acting on some analytical operators. For this purpose, we use a characterization theorem between this class of operators and their symbols. Applying the quantum Gross Laplacian to the...

- A Boundary Harnack Principle for Infinity-Laplacian and Some Related Results. Bhattacharya, Tilak // Boundary Value Problems;2008 Supplement, p1
We prove a boundary comparison principle for positive infinity-harmonic functions for smooth boundaries. As consequences, we obtain (a) a doubling property for certain positive infinity-harmonic functions in smooth bounded domains and the half-space, and (b) the optimality of blowup rates of...

- ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS. Afrouzi, G. A.; Moghaddam, M. Khaleghy; Mohammadpour, J.; Zameni, M. // Journal of Nonlinear Sciences & its Applications;2009, Vol. 2 Issue 1, p38
In this paper, we consider the following Neumann boundary value problem {-u?(x) = u3(x) - ?|u(x)|, x ? (0, 1), u'(0) = 0 = u'(1), where ? ? R is parameter. We study the positive and negative solutions of this problem with respect to a parameter ? (i.e. u(0) = ?) in all R*. By using a quadrature...

- A free-boundary problem for the evolution p-Laplacian equation with a combustion boundary condition. To, Tung // Calculus of Variations & Partial Differential Equations;Jun2009, Vol. 35 Issue 2, p239
We study the existence, uniqueness and regularity of solutions of the equation f t = ? p f = div (| Df| p-2 Df) under over-determined boundary conditions f = 0 and | Df| = 1. We show that if the initial data is concave and Lipschitz with a bounded and convex support, then the problem admits a...

- Multiple Solutions for Noncoercive Problems with the p-Laplacian. Gasinski, Leszek; Papageorgiou, Nikolaos S. // Bulletin of the Belgian Mathematical Society - Simon Stevin;Feb2010, Vol. 17 Issue 1, p83
We consider a nonlinear elliptic equation driven by the p-Laplacian and with a Carathï¿½odory right hand side nonlinearity which exhibits an asymmetric asymptotic behaviour at +8 and at -8. These hypotheses imply that the Euler functional of the problem is noncoercive (indefinite). Using...

- Geometry on Probability Spaces. Smale, Steve; Ding-Xuan Zhou // Constructive Approximation;Dec2009, Vol. 30 Issue 3, p311
Partial differential equations and the Laplacian operator on domains in Euclidean spaces have played a central role in understanding natural phenomena. However, this avenue has been limited in many areas where calculus is obstructed, as in singular spaces, and in function spaces of functions on...

- Estimates and structure of Î±-harmonic functions. Bogdan, Krzysztof; Kulezycki, Tadeusz; KwaŘnicki, Mateusz // Probability Theory & Related Fields;Mar2008, Vol. 140 Issue 3/4, p345
We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open set D. This yields a unique representation of such functions as integrals against measures on D c âˆª {âˆž} satisfying an integrability condition. The...

- Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations. Peng Chen; Hui Fang // Advances in Difference Equations;2007, p1
We obtain a sufficient condition for the existence of periodic and subharmonic solutions of second-order p-Laplacian difference equations using the critical point theory.

- Winkler plate bending problems by a truly boundary-only boundary particle method. Fu, Zhuojia; Chen, Wen; Yang, Wei // Computational Mechanics;Dec2009, Vol. 44 Issue 6, p757
This paper makes the first attempt to use the boundary particle method (BPM) to solve the problems of Winkler plate under lateral loading. In this study, we find that the standard fundamental solution does not work well with the BPM. Instead we construct the modified singular fundamental...