Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part II: The KDV Equation.
Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part I: Schrödinger Equations.
Fourier-like methods for equations with separable variables
It is well known that a power of a right invertible operator is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However, a linear combination of right invertible operators (in particular, their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The...
Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier-Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.
Four-parameter bifurcation for a -Laplacian system.
Fourth order eigenvalue approximation by extrapolation on domains with reentrant corners.
Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations.
Fourth-order nonlinear elliptic equations with critical growth
In this paper we consider a nonlinear elliptic equation with critical growth for the operator in a bounded domain . We state some existence results when . Moreover, we consider , expecially when is a ball in .
Fourth-order partial differential equations for effective image denoising.
Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.
Fractal Relaxed Dirichlet Problems.
Fractal Weyl laws for quantum resonances
Fractals and the base eigenvalue of the Laplacian on certain noncompact surfaces.
Fractals, trees and the Neumann Laplacian.
Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes
Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.Wentzell boundary value problem for pseudo-differential operators generating Markov processes but not satisfying the transmission condition are not well understood. Studying fractional derivatives and fractional powers of such operators gives some insights in this problem. Since an L^p – theory for such operators will provide a helpful tool we investigate the L^p –domains of certain model operators.* This work is partially supported...
Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations
MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf GorenfloThere is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving process, corresponding...
Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields
We study the notion of fractional -differentiability of order along vector fields satisfying the Hörmander condition on . We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different -norms are equivalent. We also prove a local embedding , where q is a suitable exponent greater than p.
Fredholm alternatives and surjectivity results for multivalued -proper and condensing mappings with applications to nonlinear integral and differential equations
Fredholm determinants
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.