Results 21 to 30 of about 417 (39)

Radial symmetry, monotonicity and Liouville theorem for Marchaud fractional parabolic equations with the nonlocal Bellman operator

Advanced Nonlinear Studies
In this article, we focus on studying space-time fractional parabolic equations with the nonlocal Bellman operator and the Marchaud fractional derivative. To address the difficulty caused by the space-time non-locality of operator ∂tα−Fs ${\partial }_{t}^
Liu Mengru, Zhang Lihong, Wang Guotao
doaj   +1 more source

Rigidity results for some boundary quasilinear phase transitions

, 2008
We consider a quasilinear equation given in the half-space, i.e. a so called boundary reaction problem. Our concerns are a geometric Poincar\'e inequality and, as a byproduct of this inequality, a result on the symmetry of low-dimensional bounded stable ...
Sire, Yannick, Valdinoci, Enrico
core   +2 more sources

Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_ ...
Yang Zerong, He Yong
doaj   +1 more source

The Fourier transform and convolutions generated by a differential operator with boundary condition on a segment

, 2013
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution explicitly depends on
Kanguzhin, Baltabek, Tokmagambetov, Niyaz   +1 more
core   +1 more source

Non-existence, radial symmetry, monotonicity, and Liouville theorem of master equations with fractional p-Laplacian

Advances in Nonlinear Analysis
In this article, first, we introduce a new operator (∂t−Δp)su(z,t)=Cn,sp∫−∞t∫Rn∣u(z,t)−u(ζ,ϱ)∣p−2(u(z,t)−u(ζ,ϱ))(t−ϱ)n2+1+sp2e−∣z−ζ∣24(t−ϱ)dζdϱ,{\left({\partial }_{t}-{\Delta }_{p})}^{s}u\left(z,t)={C}_{n,sp}\underset{-\infty }{\overset{t}{\int }}\mathop{
Liu Mengru, Zhang Lihong
doaj   +1 more source

$L_2$-Small Deviations for Weighted Stationary Processes

, 2018
We find logarithmic asymptotics of $L_2$-small deviation probabilities for weighted stationary Gaussian processes (both for real and complex-valued) having power-type discrete or continuous spectrum.
Lifshits, Mikhail, Nazarov, Alexander
core   +1 more source

Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains

, 2014
We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener-Hopf operators with discontinuous symbols. The discontinuities occur on the surfaces which are assumed to be piece-wise smooth.
Sobolev, A. V.
core   +1 more source

Bilinear pseudo-differential operators with exotic symbols, II

, 2018
The boundedness from $H^p \times L^2$ to $L^r$, $1/p+1/2=1/r$, and from $H^p \times L^{\infty}$ to $L^p$ of bilinear pseudo-differential operators is proved under the assumption that their symbols are in the bilinear H\"ormander class $BS^m_{\rho,\rho}$,
Miyachi, Akihiko, Tomita, Naohito
core   +1 more source

A topological definition of the Maslov bundle [PDF]

, 2006
We give a definition of the Maslov fibre bundle for a lagrangian submanifold of the cotangent bundle of a smooth manofold. This definition generelizes the definition given, in homotopic terms, by Arnol'd for lagrangian submanifolds of the cotangent ...
Anné, Colette
core   +2 more sources

The K-theory of bisingular pseudodifferential algebras

, 2015
In this paper we calculate the K-theory of $C^{\ast}$-algebras given by the norm-closures of spaces of bisingular pseudodifferential operators.
Bohlen, Karsten
core   +1 more source