Parabolic equations with rough data

Herbert Koch; Tobias Lamm

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 4, page 457-477
  • ISSN: 0862-7959

Abstract

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We survey recent work on local well-posedness results for parabolic equations and systems with rough initial data. The design of the function spaces is guided by tools and constructions from harmonic analysis, like maximal functions, square functions and Carleson measures. We construct solutions under virtually optimal scale invariant conditions on the initial data. Applications include BMO initial data for the harmonic map heat flow and the Ricci-DeTurck flow for initial metrics with small local oscillation. The approach is sufficiently flexible to apply to boundary value problems, quasilinear and fully nonlinear equations.

How to cite

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Koch, Herbert, and Lamm, Tobias. "Parabolic equations with rough data." Mathematica Bohemica 140.4 (2015): 457-477. <http://eudml.org/doc/271834>.

@article{Koch2015,
abstract = {We survey recent work on local well-posedness results for parabolic equations and systems with rough initial data. The design of the function spaces is guided by tools and constructions from harmonic analysis, like maximal functions, square functions and Carleson measures. We construct solutions under virtually optimal scale invariant conditions on the initial data. Applications include BMO initial data for the harmonic map heat flow and the Ricci-DeTurck flow for initial metrics with small local oscillation. The approach is sufficiently flexible to apply to boundary value problems, quasilinear and fully nonlinear equations.},
author = {Koch, Herbert, Lamm, Tobias},
journal = {Mathematica Bohemica},
keywords = {parabolic equation; rough initial data},
language = {eng},
number = {4},
pages = {457-477},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Parabolic equations with rough data},
url = {http://eudml.org/doc/271834},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Koch, Herbert
AU - Lamm, Tobias
TI - Parabolic equations with rough data
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 457
EP - 477
AB - We survey recent work on local well-posedness results for parabolic equations and systems with rough initial data. The design of the function spaces is guided by tools and constructions from harmonic analysis, like maximal functions, square functions and Carleson measures. We construct solutions under virtually optimal scale invariant conditions on the initial data. Applications include BMO initial data for the harmonic map heat flow and the Ricci-DeTurck flow for initial metrics with small local oscillation. The approach is sufficiently flexible to apply to boundary value problems, quasilinear and fully nonlinear equations.
LA - eng
KW - parabolic equation; rough initial data
UR - http://eudml.org/doc/271834
ER -

References

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