John and Uniform Domains in Generalized Siegel BoundariesSpringer Science and Business Media LLC - Tập 53 - Trang 921-945 - 2019
Roberto Monti, Daniele Morbidelli
Given the pair of vector fields X = ∂x + |z|2my∂t and Y = ∂y −|z|2mx∂t,where (x,y,t) =
, we give a condition on a bounded domain
which ensures that Ω is an (ε,δ)-domain for the Carnot-Carathéodory metric. We also analyze the Ahlfors regularity of the natural surface measure induced on ∂Ω by the vector fields.
Geometry of Prime End Boundary and the Dirichlet Problem for Bounded Domains in Metric Measure SpacesSpringer Science and Business Media LLC - Tập 42 - Trang 335-363 - 2014
Dewey Estep, Nageswari Shanmugalingam
In this note we study the Dirichlet problem associated with a version of prime end boundary of a bounded domain in a complete metric measure space equipped with a doubling measure supporting a Poincaré inequality. We show the resolutivity of functions that are continuous on the prime end boundary and are Lipschitz regular when restricted to the subset of all prime ends whose impressions are single...... hiện toàn bộ
Potential Theory on Minimal Hypersurfaces I: Singularities as Martin BoundariesSpringer Science and Business Media LLC - Tập 53 - Trang 1493-1528 - 2019
Joachim Lohkamp
Area minimizing hypersurfaces and, more generally, almost minimizing hypersurfaces frequently occur in geometry, dynamics and physics. A central problem is that a general (almost) minimizing hypersurface H contains a complicated singular set Σ. Regardless of this we can develop a detailed potential theory on H ∖Σ applicable to large classes of linear elliptic second order operators. We even get a ...... hiện toàn bộ
The Smoothness of Laws of Random Flags and Oseledets Spaces of Linear Stochastic Differential EquationsSpringer Science and Business Media LLC - - 1998
Peter Imkeller
The Oseledets spaces of a random dynamical system generated by a linear stochastic differential equation are obtained as intersections of the corresponding nested invariant spaces of a forward and a backward flag, described as the stationary states of flows on corresponding flag manifolds. We study smoothness of their laws and conditional laws by applying Malliavin's calculus. If the Lie algebras ...... hiện toàn bộ
On the Asymptotic Dirichlet Problem for the Minimal Hypersurface Equation in a Hadamard ManifoldSpringer Science and Business Media LLC - - 2017
Jean-Baptiste Casteras, Ilkka Holopainen, Jaime B. Ripoll
We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold M of dimension n ≥ 2 for a large class of operators containing, in particular, the p-Laplacian and the minimal graph operator. We extend several existence results obtained for the p-Laplacian to our class of operators. As an application of our main result, we prove the solvability of the asymptotic Dirichlet problem for the m...... hiện toàn bộ