Displaying 21 – 40 of 208

Showing per page

Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian

Sundararaja Ramaswamy (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The aim of this paper is to characterize the u.s.c. (resp. l.s.c.) viscosity sub (resp. super) solutions of the Laplacian which do not take the value + (resp. - ) as precisely the sub (resp. super) harmonic functions.

Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators

Dario Daniele Monticelli (2010)

Journal of the European Mathematical Society

We deal with maximum principles for a class of linear, degenerate elliptic differential operators of the second order. In particular the Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypothesis on the degeneracy set of the operator. We derive, as consequences of these principles, some generalized maximum principles and an a priori estimate on the solutions of the Dirichlet problem for the linear equation....

Mean curvature properties for p -Laplace phase transitions

Berardino Sciunzi, Enrico Valdinoci (2005)

Journal of the European Mathematical Society

This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of p -Laplacian type and a double well potential h 0 with suitable growth conditions. We prove that level sets of solutions of Δ p u = h 0 ' ( u ) possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.

Currently displaying 21 – 40 of 208