eBook ISBN:  9781470403126 
Product Code:  MEMO/151/719.E 
List Price:  $56.00 
MAA Member Price:  $50.40 
AMS Member Price:  $33.60 
eBook ISBN:  9781470403126 
Product Code:  MEMO/151/719.E 
List Price:  $56.00 
MAA Member Price:  $50.40 
AMS Member Price:  $33.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 151; 2001; 113 ppMSC: Primary 42; 35
In this memoir we consider the Dirichlet problem for parabolic operators in a half space with singular drift terms. In chapter I we begin the study of a parabolic PDE modeled on the pullback of the heat equation in certain time varying domains considered by LewisMurray and HofmannLewis. In chapter II we obtain mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the \(L^q(R^n)\) Dirichlet problem for these PDE's has a solution when \(q\) is large enough. In chapter III we prove an analogue of a theorem of Fefferman, Kenig, and Pipher for certain parabolic PDE's with singular drift terms. Each of the chapters that comprise this memoir has its own numbering system and list of references.
ReadershipGraduate students and research mathematicians interested in Fourier analysis and partial differential equations.

Table of Contents

Chapters

I. The dirichlet problem and parabolic measure

II. Absolute continuity and the $L^p$ dirichlet problem: Part 1

III. Absolute continuity and the $L^p$ dirichlet problem: Part 2


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In this memoir we consider the Dirichlet problem for parabolic operators in a half space with singular drift terms. In chapter I we begin the study of a parabolic PDE modeled on the pullback of the heat equation in certain time varying domains considered by LewisMurray and HofmannLewis. In chapter II we obtain mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the \(L^q(R^n)\) Dirichlet problem for these PDE's has a solution when \(q\) is large enough. In chapter III we prove an analogue of a theorem of Fefferman, Kenig, and Pipher for certain parabolic PDE's with singular drift terms. Each of the chapters that comprise this memoir has its own numbering system and list of references.
Graduate students and research mathematicians interested in Fourier analysis and partial differential equations.

Chapters

I. The dirichlet problem and parabolic measure

II. Absolute continuity and the $L^p$ dirichlet problem: Part 1

III. Absolute continuity and the $L^p$ dirichlet problem: Part 2