The Resource The poisson problem on Lipschitz domains, by Svitlana Mayboroda, (electronic resource)

The poisson problem on Lipschitz domains, by Svitlana Mayboroda, (electronic resource)

Label
The poisson problem on Lipschitz domains
Title
The poisson problem on Lipschitz domains
Statement of responsibility
by Svitlana Mayboroda
Creator
Contributor
Thesis advisor
Subject
Genre
Language
eng
Summary
The aim of this work is to describe the sharp ranges of indices, for which the Poisson problem for Laplacian with Dirichlet or Neumann boundary conditions is well-posed on the scales of Besov and Triebel-Lizorkin spaces on arbitrary Lipschitz domains. The main theorems we prove extend the work of D. Jerison and C. Kenig [JFA, 95], whose methods and results are largely restricted to the case p_ 1, and answer the open problem #3.2.21 on p. 121 in C. Kenig's book in the most complete fashion. When specialized to Hardy spaces, our results provide a solution of a (strengthened form of a) conjecture made by D.-C. Chang, S.Krantz and E. Stein regarding the regularity of the Green potentials on Hardy spaces in Lipschitz domains. The corollaries of our main results include new proofs and various extensions of: Hardy space estimates for Green potentials in convex domains due to V. Adolfsson, B.Dahlberg, S. Fromm, D. Jerison, G.Verchota and T.Wolff and the Lp - Lq estimates for the gradients of Green potentials in Lipschitz domains, due to B. Dahlberg
Cataloging source
MUU
http://library.link/vocab/creatorName
Mayboroda, Svitlana
Degree
Ph.D.
Dissertation year
2005.
Granting institution
University of Missouri-Columbia
Index
no index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
  • theses
http://library.link/vocab/relatedWorkOrContributorName
Mitrea, Marius
http://library.link/vocab/subjectName
  • Poisson's equation
  • Lipschitz spaces
  • Functions of complex variables
Target audience
specialized
Label
The poisson problem on Lipschitz domains, by Svitlana Mayboroda, (electronic resource)
Instantiates
Publication
Note
  • The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file
  • Title from title screen of research.pdf file viewed on (January 25, 2007)
  • Vita
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
80018163
Dimensions
unknown
Form of item
electronic
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System details
Mode of access: World Wide Web
Label
The poisson problem on Lipschitz domains, by Svitlana Mayboroda, (electronic resource)
Publication
Note
  • The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file
  • Title from title screen of research.pdf file viewed on (January 25, 2007)
  • Vita
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
80018163
Dimensions
unknown
Form of item
electronic
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System details
Mode of access: World Wide Web

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