Harnack's Inequality for Elliptic Differential Equations on Minimal Surfaces.
E. Bombieri, E. Giusti (1971/1972)
Inventiones mathematicae
Karl-Theodor Sturm (1994)
Mathematische Zeitschrift
Pietro Zamboni (1993)
Rendiconti del Seminario Matematico della Università di Padova
Ahmed Mohammed (2002)
Revista Matemática Iberoamericana
We prove Harnack's inequality for non-negative solutions of some degenerate elliptic operators in divergence form with the lower order term coefficients satisfying a Kato type contition.
Mařík, Robert (2000)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
D. Gogny, P. L. Lions (1986)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Josef Král (1990)
Pokroky matematiky, fyziky a astronomie
Zayed, E.M.E. (1997)
International Journal of Mathematics and Mathematical Sciences
Zayed, E.M.E. (1991)
Portugaliae mathematica
Zayed, E.M.E. (1990)
International Journal of Mathematics and Mathematical Sciences
Panayiotis M. Vlamos (1999)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Gagnidze, Avtandil (1998)
Memoirs on Differential Equations and Mathematical Physics
Harold Donnelly (1975)
Inventiones mathematicae
Chang Kung-Ching (1989)
Annales de l'I.H.P. Analyse non linéaire
M. Van den Berg (2007)
Annales de l'I.H.P. Probabilités et statistiques
E.B. Davies, M. van den Berg (1989)
Mathematische Zeitschrift
Santiago R. Simanca (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let be a closed polarized complex manifold of Kähler type. Let be the maximal compact subgroup of the automorphism group of . On the space of Kähler metrics that are invariant under and represent the cohomology class , we define a flow equation whose critical points are the extremal metrics,i.e.those that minimize the square of the -norm of the scalar curvature. We prove that the dynamical system in this space of metrics defined by the said flow does not have periodic orbits, and that its...
Nick Dungey (2005)
Publicacions Matemàtiques
Let G be a Lie group. The main new result of this paper is an estimate in L2 (G) for the Davies perturbation of the semigroup generated by a centered sublaplacian H on G. When G is amenable, such estimates hold only for sublaplacians which are centered. Our semigroup estimate enables us to give new proofs of Gaussian heat kernel estimates established by Varopoulos on amenable Lie groups and by Alexopoulos on Lie groups of polynomial growth.
E. Brian Davies (1995)
Journées équations aux dérivées partielles
Nick Dungey (2005)
Studia Mathematica
Let G be a Lie group of polynomial volume growth. Consider a differential operator H of order 2m on G which is a sum of even powers of a generating list of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list which is sufficient to ensure that the semigroup kernel of H satisfies global Gaussian estimates for all times. For G not necessarily solvable, we state an analytic condition on the list which is necessary and sufficient for global Gaussian estimates....