• 沒有找到結果。

to approach the unique continuation in harmonic function and then in elliptic equations

N/A
N/A
Protected

Academic year: 2021

Share "to approach the unique continuation in harmonic function and then in elliptic equations"

Copied!
1
0
0

加載中.... (立即查看全文)

全文

(1)

1

1. Introduction

The unique continuation property has been studied in the recent years. In 1939 Cale-

man first proved unique continuation for the Schr¨ odinger operator H = 4 + V in R

2

with a bounded potential V . F.J. Almgren, Jr., [Alm79] presented a frequency function

to approach the unique continuation in harmonic function and then in elliptic equations

by N. Garofalo and F.H. Lin, [GL86] and [GL87]. C.C. Poon [Poo96] and L.Escauriaza

and J. Fernandez [EF03] modified the method to prove the unique continuation for par-

abolic equations. We follow the method to construct a modified frequency function for

degenerate parabolic equation to obtain the unique continuation property. In Section 4

we consider porous medium equation is oscillatory or not. We use Riccati transformation

for positive solutions in exterior domains in Euclidean n-space and obtain a sufficient

conditions for equations to be oscillatory by contradiction. This method is used to study

the oscillation of elliptic equations by E.S. Noussair and C.A. Swanson [NS80] and the

oscillation of p-Laplacian equation by Zhiting Xu [Xu00].

參考文獻

相關文件

Wang, Unique continuation for the elasticity sys- tem and a counterexample for second order elliptic systems, Harmonic Analysis, Partial Differential Equations, Complex Analysis,

One of the main results is the bound on the vanishing order of a nontrivial solution to the Stokes system, which is a quantitative version of the strong unique continuation prop-

Vessella, Quantitative estimates of unique continuation for parabolic equa- tions, determination of unknown time-varying boundaries and optimal stability estimates, Inverse

In this paper, we propose a practical numerical method based on the LSM and the truncated SVD to reconstruct the support of the inhomogeneity in the acoustic equation with

GCG method is developed to minimize the residual of the linear equation under some special functional.. Therefore, the minimality property does not hold... , k) in order to construct

Now, nearly all of the current flows through wire S since it has a much lower resistance than the light bulb. The light bulb does not glow because the current flowing through it

Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach.. Based on the geometric properties

● Using canonical formalism, we showed how to construct free energy (or partition function) in higher spin theory and verified the black holes and conical surpluses are S-dual.