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The Technion school lecture notes:the moving plane method,or doing PDEs in a cafe
Technion school lecture notes moving plane method doing PDEs a cafe
2015/7/14
We will have two main characters in these notes: the maximum principle and the sliding method. The latter has a twin, the moving plane method–they are often so indistinguishable that we will count the...
Unique continuation for a quasilinear elliptic equation in the plane
Dead core Harnack inequality maximum principle nodal domain p-Laplacian p-harmonic quasilinear elliptic equation
2012/6/27
We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions. We show that if the boundary data has finite number of relative maxima and minima t...
Point measurements for a Neumann-to-Dirichlet map and the Calderón problem in the plane
Calderon problem Neumann-to-Dirichlet map point measurements Analysis of PDEs
2012/4/18
This work considers properties of the Neumann-to-Dirichlet map for the conductivity equation under the assumption that the conductivity is identically one close to the boundary of the examined smooth,...
The Kadomtsev-Petviashvili I Equation on the Half-Plane
Kadomtsev-Petviashvili Half-Plane Analysis of PDEs
2011/9/22
Abstract: A new method for the solution of initial-boundary value problems for \textit{linear} and \textit{integrable nonlinear} evolution PDEs in one spatial dimension was introduced by one of the au...
KdV equation in the quarter--plane: evolution of the Weyl functions and unbounded solutions
KdV initial–boundary value problem Weyl function evolution low–energy asymptotics blow–up solution
2011/9/1
Abstract: The matrix KdV equation with a negative dispersion term is considered in the right upper quarter--plane. The evolution law is derived for the Weyl function of a corresponding auxiliary linea...
Asymptotics of visibility in the hyperbolic plane
Boolean model hyperbolic geometry visibility Poincar´ e disc
2011/2/25
At each point of a Poisson point process of intensity in the hyperbolic place, center a ball of bounded random radius. Consider the probability Pr that from a fixed point, there is some direction in...
Determinantal representation and subschemes of general plane curves
Determinantal representation subschemes of general plane curves
2011/2/21
Let M = (mij ) be an n × n square matrix of integers. For our purposes, we can assume without loss of generality that M is homogeneous and that the entries are non-increasing going leftward and downwa...
On a General Linear Nonlocal Curvature Flow of Convex Plane Curves
General Linear Nonlocal Curvature Flow Convex Plane Curves
2011/1/17
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal cur-vature flow for convex closed plane curves and discuss the short time existence and asymptotic
convergence behavio...
Relative Node Polynomials for Plane Curves
Enumerative geometry floor diagram Gromov-Witten theory
2010/12/13
We generalize the recent work of S. Fomin and G. Mikhalkin on polynomial formulas for Severi degrees.
Contracting Convex Immersed Closed Plane Curves with Slow Speed of Curvature
Convex Immersed Closed Plane Curves Slow Speed of Curvature
2010/12/13
We study the contraction of a convex immersed plane curve with speed 1 k , where ∈ (0, 1] is a constant and show that, if the blow-up rate of the curvature is of type one, it will converge to a homo...
Isometric Immersions of the Hyperbolic Plane into the Hyperbolic Space
hyperbolic space developable surface null curve K¨ahler and para-K¨ahler structure
2010/12/9
In this paper, we parametrize the space of isometric immersions of the hyperbolic plane into the hyperbolic 3-space in terms of null-causal curves in the space of oriented geodesics. Moreover, we char...
On quasiconformal selfmappings of the unit disk and elliptic PDE in the plane
Quasiconformal maps Beltrami equation Elliptic PDE Lipschitz condition
2010/11/30
In this paper we prove the following theorem: if w is a quasiconformal mapping of the unit disk onto itself satisfying elliptic partial differential inequality |L[w]| ≤ B|∇w|2 + , then...
On a plane section of an integral curve in positive characteristic
Integral curve plane section minimal curve positive characteristic
2010/12/9
If C P3 k is an integral curve and k an algebraically closed field of characteristic 0, it is known that the points of the general plane section C \H of C are in uniform position. From this it follo...
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
class of two-dimensional nonlocal nonlinear wave equatio elastic materials
2010/12/1
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing antiplane shear motions in nonlocal elasticity.
<正> 1.Introduction.Let the tangent surface of an analytic curve Cin ordinary space be cut by a plane through a tangent at an ordinarypoint O of C,then the plane section thus obtained has a point of in...