相关论文: The Maximum Principle for the Bergman Space and th…
Several uncertainty principles are proved for the Fock space.
We give a quick and direct proof of the strong maximum principle on finite dimensional $RCD$ spaces based on the Laplacian comparison of the squared distance.
Let $A^2(D)$ be the Bergman space over the open unit disk $D$ in the complex plane. Korenblum conjectured that there is an absolute constant $c \in (0,1)$ such that whenever $|f(z)|\le |g(z)|$ in the annulus $c<|z|<1$ then $||f(z)|| \le…
We establish a boundary maximum principle for free boundary minimal submanifolds in a Riemannian manifold with boundary, in any dimension and codimension. Our result holds more generally in the context of varifolds.
This note shows that in Bauer's maximum principle, the assumed convexity of the objective function can be relaxed to quasiconvexity.
The maximum principle for SPDEs is established in multidimensional $C^{1}$ domains. An application is given to proving the H\"older continuity up to the boundary of solutions of one-dimensional SPDEs.
In this paper we obtain new estimates of the sequential Caputo fractional derivatives of a function at its extremum points. We derive comparison principles for the linear fractional differential equations, and apply these principles to…
In this survey we formulate our results on different forms of maximum principles for linear elliptic equations and systems. We start with necessary and sufficient conditions for validity of the classical maximum modulus principle for…
In this paper, maximum principles for Euclidean and hyperbolic discrete conformal structures on polyhedral surfaces are established. These maximum principles unify and generalize the maximum principles for vertex scalings and different…
We consider eigenvalue problems for general elliptic operators of arbitrary order subject to homogeneous boundary conditions on open subsets of the euclidean N-dimensional space. We prove stability results for the dependence of the…
The newly discovered principle of maximum force makes it possible to summarize special relativity, quantum theory\se, and general relativity in one fundamental limit principle each. The three principles fully contain the three theories and…
An annulus is, informally, a ring-shaped region, often described by two concentric circles. The maximum-width empty annulus problem asks to find an annulus of a certain shape with the maximum possible width that avoids a given set of $n$…
For the classical space of functions with bounded mean oscillation, it is well known that VMO** = BMO and there are many characterizations of the distance from a function f in BMO to VMO. When considering the Bloch space, results in the…
We prove an avoidance principle for expanding translates of unipotent orbits for some semisimple homogeneous spaces. In addition, we prove a quantitative isolation result of closed orbits and give an upper bound on the number of closed…
This study explores the cosmological constant problem and modified uncertainty principle within a unified framework inspired by a void-dominated scenario. In a recent paper~\cite{Yusofi:2022hgg}, voids were modeled as spherical bubbles of…
In this paper, we establish the following Liouville theorem for fractional \emph{p}-harmonic functions. {\em Assume that $u$ is a bounded solution of $$(-\lap)^s_p u(x) = 0, \;\; x \in \mathbb{R}^n,$$ with $0<s<1$ and $p \geq 2$. Then $u$…
We establish an explicit maximum principle for the Dirichlet problem associated with the $p$-Laplacian ($p>1$), where the constant depends on both $p$ and the geometry of the domain. From this result we derive two main applications. First,…
We discuss a conjectural duality between hyperbolic spaces on one hand and spacetimes on the other hand, living on the opposite sides of the common absolute. This duality goes via M\"obius structures on the absolute, and it is easily…
In this paper we deal with the care one must have in adopting approximations in regard with terms he chooses to leave behind in the particular case of the expression valid for the maximum period of a long pendulum oscillating near Earth's…
The law of balance of angular momentum is shown to imply the existence of absolute time, a fundamental physical quantity that is independent of the motion or position of the observer. Absolute time implies the notion of absolute…