اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPhragmen-Lindelof theorem for infinity harmonic functions
132
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate a version of the Phragmen-Lindelof theorem for solutions of the equation $Delta_infty u=0$ in unbounded convex domains. The method of proof is to consider this infinity harmonic equation as the limit of the $p$-harmonic equation when $p$ tends to $infty$.
قيم البحث
اقرأ أيضاً
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from geometric dat
a. As a by-product, it is shown that the evolution of the gradient of a harmonic function along the gradient flow is determined by the mean curvature of the level sets that the flow intersects.
We propose a new notion called emph{infinity-harmonic maps}between Riemannain manifolds. These are natural generalizations of the well known notion of infinity harmonic functions and are also the limiting case of $p$% -harmonic maps as $pto infty $.
Infinity harmoncity appears in many familiar contexts. For example, metric projection onto the orbit of an isometric group action from a tubular neighborhood is infinity harmonic. Unfortunately, infinity-harmonicity is not preserved under composition. Those infinity harmonic maps that always preserve infinity harmonicity under pull back are called infinity harmonic morphisms. We show that infinity harmonic morphisms are precisely horizontally homothetic mas. Many example of infinity-harmonic maps are given, including some very important and well-known classes of maps between Riemannian manifolds.
We study energy measures on SG based on harmonic functions. We characterize the positive energy measures through studying the bounds of Radon-Nikodym derivatives with respect to the Kusuoka measure. We prove a limited continuity of the derivative on
the graph $V_*$ and express the average value of the derivative on a whole cell as a weighted average of the values on the boundary vertices. We also prove some characterizations and properties of the weights.
For an infinite penny graph, we study the finite-dimensional property for the space of harmonic functions, or ancient solutions of the heat equation, of polynomial growth. We prove the asymptotically sharp dimensional estimate for the above spaces.
We show that tensor products of $k$ gradients of harmonic functions, with $k$ at least three, are dense in $C(overline{Omega})$, for any bounded domain $Omega$ in dimension 3 or higher. The bulk of the argument consists in showing that any smooth com
pactly supported $k$-tensor that is $L^2$-orthogonal to all such products must be zero. This is done by using a Gaussian quasi-mode based construction of harmonic functions in the orthogonality relation. We then demonstrate the usefulness of this result by using it to prove uniqueness in the inverse boundary value problem for a coupled quasilinear elliptic system. The paper ends with a discussion of the corresponding property for products of two gradients of harmonic functions, and the connection of this property with the linearized anisotropic Calderon problem.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
