# The ${L}^{p}$ Neumann problem for the heat equation in non-cylindrical domains

Journées équations aux dérivées partielles (1998)

- page 1-7
- ISSN: 0752-0360

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topHofmann, Steve, and Lewis, John L.. "The ${L}^p$ Neumann problem for the heat equation in non-cylindrical domains." Journées équations aux dérivées partielles (1998): 1-7. <http://eudml.org/doc/93363>.

@article{Hofmann1998,

abstract = {I shall discuss joint work with John L. Lewis on the solvability of boundary value problems for the heat equation in non-cylindrical (i.e., time-varying) domains, whose boundaries are in some sense minimally smooth in both space and time. The emphasis will be on the Neumann problem with data in $L^p$. A somewhat surprising feature of our results is that, in contrast to the cylindrical case, the optimal results hold when $p=2$, with the situation getting progressively worse as $p$ approaches $1$. In particular, in our setting, the Neumann problem fails to be solvable when the data is taken to belong to the Hardy space $H^1$.},

author = {Hofmann, Steve, Lewis, John L.},

journal = {Journées équations aux dérivées partielles},

keywords = {minimally smooth boundary; Neumann problem with data in ; Hardy space},

language = {eng},

pages = {1-7},

publisher = {Université de Nantes},

title = {The $\{L\}^p$ Neumann problem for the heat equation in non-cylindrical domains},

url = {http://eudml.org/doc/93363},

year = {1998},

}

TY - JOUR

AU - Hofmann, Steve

AU - Lewis, John L.

TI - The ${L}^p$ Neumann problem for the heat equation in non-cylindrical domains

JO - Journées équations aux dérivées partielles

PY - 1998

PB - Université de Nantes

SP - 1

EP - 7

AB - I shall discuss joint work with John L. Lewis on the solvability of boundary value problems for the heat equation in non-cylindrical (i.e., time-varying) domains, whose boundaries are in some sense minimally smooth in both space and time. The emphasis will be on the Neumann problem with data in $L^p$. A somewhat surprising feature of our results is that, in contrast to the cylindrical case, the optimal results hold when $p=2$, with the situation getting progressively worse as $p$ approaches $1$. In particular, in our setting, the Neumann problem fails to be solvable when the data is taken to belong to the Hardy space $H^1$.

LA - eng

KW - minimally smooth boundary; Neumann problem with data in ; Hardy space

UR - http://eudml.org/doc/93363

ER -

## References

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