The $L^{p}$ regularity problem for the heat equation in non-cylindrical domains
Hofmann, Steven ; Lewis, John L.
Illinois J. Math., Tome 43 (1999) no. 3, p. 752-769 / Harvested from Project Euclid
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We consider the Dirichlet problem for the heat equation in domains with a minimally smooth, time-varying boundary. Our boundary data is taken to belong to a parabolic Sobolev space having a tangential (spatial) gradient, and $1/2$ of a time derivative, in $L^{p}$, $1 \lt p \lt 2 + \epsilon$. We obtain sharp $L^{p}$ estimates for the parabolic non-tangential maximal function of the gradient of our solutions.
Publié le : 1999-12-15
Classification:  35K05,  31B10,  35B65 
@article{1256060690,
     author = {Hofmann, Steven and Lewis, John L.},
     title = {The $L^{p}$ regularity problem for the heat equation in non-cylindrical domains},
     journal = {Illinois J. Math.},
     volume = {43},
     number = {3},
     year = {1999},
     pages = { 752-769},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256060690}
}

Hofmann, Steven; Lewis, John L. The $L^{p}$ regularity problem for the heat equation in non-cylindrical domains. Illinois J. Math., Tome 43 (1999) no. 3, pp.  752-769. http://gdmltest.u-ga.fr/item/1256060690/