scholarly journals Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators

2014 ◽  
Vol 28 (2) ◽  
pp. 483-529 ◽  
Author(s):  
Steve Hofmann ◽  
Carlos Kenig ◽  
Svitlana Mayboroda ◽  
Jill Pipher
Keyword(s):  
Dirichlet Problem ◽  
Maximal Function ◽  
Elliptic Operators ◽  
Square Function

scholarly journals Weak Uniqueness for Elliptic Operators in ℝ3 with Time-Independent Coefficients

2006 ◽  
Vol 74 (1) ◽  
pp. 91-100
Author(s):  
Cristina Giannotti
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Operator ◽  
Elliptic Operators ◽  
Second Order ◽  
Weak Uniqueness

The author gives a proof with analytic means of weak uniqueness for the Dirichlet problem associated to a second order uniformly elliptic operator in ℝ3 with coefficients independent of the coordinate x3 and continuous in ℝ2 {0}.

Multi-parameter Carnot-Carath´eodory Geometry

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Singular Integral ◽  
Maximal Function ◽  
Integral Operators ◽  
Product Type ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Square Function ◽  
Frobenius Theorem ◽  
Parameter Theory

This chapter develops the theory of multi-parameter Carnot–Carathéodory geometry, which is needed to study singular integral operators. In the case when the balls are of product type, all of the results are simple variants of results in the single-parameter theory. When the balls are not of product type, these ideas become more difficult. What saves the day is the quantitative Frobenius theorem given in Chapter 2. This can be used to estimate certain integrals, as well as develop an appropriate maximal function and an appropriate Littlewood–Paley square function, all of which are essential to our study of singular integral operators.

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