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The Dirichlet problem for standard weighted Laplacians in the upper half plane

Carlsson, Marcus LU and Wittsten, Jens (2016) In Journal of Mathematical Analysis and Applications 436(2). p.868-889
Abstract
In this paper the Dirichlet problem for a class of standard weighted Laplace operators in the upper half plane is solved by means of a counterpart of the classical Poisson integral formula. Boundary limits and representations of the associated solutions are studied within a framework of weighted spaces of distributions. Special attention is given to the development of a, suitable uniqueness theory for the Dirichlet problem under appropriate growth constraints at infinity. (C) 2015 Elsevier Inc. All rights reserved.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Poisson integral, Weighted Laplace operator, Poisson kernel, Weighted, space of distributions
in
Journal of Mathematical Analysis and Applications
volume
436
issue
2
pages
868 - 889
publisher
Academic Press
external identifiers
  • wos:000368974100016
  • scopus:84955204354
ISSN
0022-247X
DOI
10.1016/j.jmaa.2015.12.026
language
English
LU publication?
yes
id
438f3f70-316c-41e1-b79b-0647d4d3fc17 (old id 8728494)
date added to LUP
2016-04-01 12:56:53
date last changed
2025-04-04 14:41:31
@article{438f3f70-316c-41e1-b79b-0647d4d3fc17,
  abstract     = {{In this paper the Dirichlet problem for a class of standard weighted Laplace operators in the upper half plane is solved by means of a counterpart of the classical Poisson integral formula. Boundary limits and representations of the associated solutions are studied within a framework of weighted spaces of distributions. Special attention is given to the development of a, suitable uniqueness theory for the Dirichlet problem under appropriate growth constraints at infinity. (C) 2015 Elsevier Inc. All rights reserved.}},
  author       = {{Carlsson, Marcus and Wittsten, Jens}},
  issn         = {{0022-247X}},
  keywords     = {{Poisson integral; Weighted Laplace operator; Poisson kernel; Weighted; space of distributions}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{868--889}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Mathematical Analysis and Applications}},
  title        = {{The Dirichlet problem for standard weighted Laplacians in the upper half plane}},
  url          = {{http://dx.doi.org/10.1016/j.jmaa.2015.12.026}},
  doi          = {{10.1016/j.jmaa.2015.12.026}},
  volume       = {{436}},
  year         = {{2016}},
}