Thierry Coulhon, Adam Sikora
We prove that in presence of $L^2$ Gaussian estimates, so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.
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We study Phragmén-Lindelöf properties of viscosity solutions to a class of doubly nonlinear parabolic equations in $\mathbb{R}^n\times (0,T)$. We also include an application to some doubly nonlinear equations.
We investigate a version of the Phragmén-Lindelöf theorem for solutions of the equation $Δ_\infty u=0$ 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 $\infty$.
Phragmèn-Lindelöf type theorems for parabolic equations on infinite graphs
针对带变密度的抛物型方程柯西问题，在组合无限加权图上建立了Phragmèn-Lindelöf原理，并证明了密度假设的最优性。
We study Phragmén-Lindelöf properties for viscosity solutions to a class of nonlinear parabolic equations of the type $H(Du, D^2u+Z(u)Du\otimes Du)+χ(t)|Du|^σ-u_t=0$ under a certain boundedness condition on $H$. We also state results for positive solutions to a class of doubly nonlinear equation $H(Du, D^2u)-f(u)u_t=0$.
Paper dedicated to qualitative study of the solution of the Zaremba type problem in Lipschitz domain with respect to the elliptic equation in non-divergent form. Main result is Landis type Growth Lemma in spherical layer for Mixed Boundary Value Problem in the class of "admissible domain". Based on the Growth Lemma Phragmén-Lindelöf theorem is proved at junction point of Dirichlet boundary and boundary over which derivative in non-tangential direction is defined.
We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $Ω\subset \mathbb R^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along the bounded directions of $Ω$, with possible degeneracy along the unbounded directions.
We prove estimates of a $p$-harmonic measure, $p \in (n-m, \infty]$, for sets in $\mathbf{R}^n$ which are close to an $m$-dimensional hyperplane $Λ\subset \mathbf{R}^n$, $m \in [0,n-1]$. Using these estimates, we derive results of Phragmén-Lindelöf type in unbounded domains $Ω\subset \mathbf{R}^n\setminus Λ$ for $p$-subharmonic functions. Moreover, we give local and global growth estimates for $p$-harmonic functions, vanishing on sets in $\mathbf{R}^n$, which are close to an $m$-dimensional hyperplane.
Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes
本文研究齐次De Giorgi类中函数的Phragmén-Lindelöf型定理，证明最大模具有幂式增长阶$\alpha\in(0,1)$，并通过反例说明$\alpha$不能达到1。
We consider fractional Schrödinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragmén-Lindelöf theorem for polynomially bounded functions on the right complex half-plane. The interpolation leads to possibly nonoptimal off-diagonal bounds.
Phragmèn-Lindelöf type theorems for elliptic equations on infinite graphs
本文研究无限图上带势椭圆方程的Phragmèn-Lindelöf原理，在适当增长条件下证明解的唯一性，并讨论条件最优性。
We prove versions of the Phragmén--Lindelöf strong maximum principle for generalized analytic functions defined on unbounded domains. A version of Hadamard's three-lines theorem is also derived.
We establish two Phragmén--Lindelöf theorems for a fully nonlinear elliptic equation. We consider a dynamic boundary condition that includes both spatial variable and time derivative terms. As a spatial term, we consider a non-linear Neumann-type operator with a strict monotonicity in the normal direction of the boundary on the spatial derivative term. Our first result is for an elliptic equation on an epigraph in $\mathbb{R}^n$. Because we assume a good structural condition, which includes wide classes of elliptic equations as well as uniformly elliptic equations, we can benefit from the stro…
On the Phragmén-Lindelöf and the superposition principles for the $p$-Laplacian
本文针对 $p$-Laplace 型椭圆方程建立叠加原理，并发展 Phragmén-Lindelöf 比较原理，应用于 Hardy 型势以改进上下解的估计。
Some counterparts of theorems of Phragmén-Lindelöf and of Ahlfors are proved for differential forms of ${\cal WT}$--classes.}
We present a Phragmén-Lindelöf type theorem with a flavor of Nevanlinna's theorem for subharmonic functions with frequent oscillations between zero and one. We use a technique inspired by a paper of Jones and Makarov.
We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragmén-Lindelöf theorem and use Fourier series to obtain a discrete analog of the three-line theorem for the gradients of harmonic functions in a strip. Then we derive estimates for the discrete harmonic measure and use elementary spectral inequalities to obtain stability estimates for Dirichlet problem in cylinder domains.
Partial data inverse problems for reaction-diffusion and heat equations
本文研究了具有未知时间依赖系数的线性和非线性抛物型方程的部分数据反问题，证明了半线性反应-扩散方程的唯一性及热方程部分Dirichlet-to-Neumann映射Fréchet导数的单射性，核心方法基于球面准模渐近族与加权Laplace变换分析。
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