<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f3.xsl"?>
<top_article>
<mrnumber>MR1913679</mrnumber>
<author>Kazuya HAYASIDA and Masatomo KOBAYASHI</author>
<author_utf8>Kazuya HAYASIDA and Masatomo KOBAYASHI</author_utf8>
<title>On $L^p$ Regularity for Weak Derivatives of Spherically Symmetric Solutions of the Porous Media Equation</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>45</volume>
<year>2002</year>
<page>23--51</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/vol45/fe45-1-2.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR1913679</mathsci_link>
<fesi_info>
  <FILE>45-23</FILE>
  <YEAR>2002</YEAR>
  <TITLE>On $L^p$ Regularity for Weak Derivatives of Spherically Symmetric Solutions of the Porous Media Equation</TITLE>
  <AUTHOR>Kazuya HAYASIDA and Masatomo KOBAYASHI</AUTHOR>
  <AUTHOR_utf8>Kazuya HAYASIDA and Masatomo KOBAYASHI</AUTHOR_utf8>
</fesi_info>

<references>

<article>
<bibitem>1</bibitem>
<author>Aronson, D. G.; B&#233;nilan, P.</author>
<title>R&#233;gularit&#233; des solutions de l'&#233;quation des mileu poreux dans $R^N$</title>
<journal>C. R. Acad. Sci. Paris, S&#233;r. A</journal>
<vol>288</vol>
<year>1979</year>
<page>103-105</page>
<mr>MR0524760</mr>
</article>

<article>
<bibitem>2</bibitem>
<author>B&#233;nilan, P.</author>
<title>A strong regularity $L^p$ for solution of the porous media equation</title>
<journal>Research Notes in Mathematics Pitman London</journal>
<vol>89</vol>
<year>1983</year>
<page>39-58</page>
<mr>MR0730795</mr>
</article>

<article>
<bibitem>3</bibitem>
<author>Caffarelli, L. A.; Friedman, A.</author>
<title>Regularity of the free boundary of a gas flow in $n$-dimensional porous medium</title>
<journal>Indiana Univ. Math. J.</journal>
<vol>29</vol>
<year>1980</year>
<page>361-369</page>
<mr>MR0570687</mr>
</article>

<article>
<bibitem>4</bibitem>
<author>Hayasida, K.</author>
<title>On the regularity properties for solutions of the Cauchy problem for the porous media equaion</title>
<journal>Proc. Amer. Math. Soc.</journal>
<vol>107</vol>
<year>1989</year>
<page>107-112</page>
<mr>MR0948150</mr>
</article>

<article>
<bibitem>5</bibitem>
<author>Hayasida, K.</author>
<title>Barenblatt solution and spherically symmetric solution of the porous media equation</title>
<journal>Applicable Analysis</journal>
<vol>69</vol>
<year>1998</year>
<page>387-407</page>
<mr>MR1706518</mr>
</article>

<article>
<bibitem>6</bibitem>
<author>Kalashnikov, A. S.</author>
<title>Some problem of the qualitative theory of non-linear degenerate second-order parabolic equation</title>
<journal>Russian Math. Surveys</journal>
<vol>42</vol>
<year>1987</year>
<page>169-222</page>
<mr>MR0898624</mr>
</article>

<book>
<bibitem>7</bibitem>
<author>Ladyzhenskaja, O. A.; Solonnikov, V. A.; Ural'ceva, N. N.</author>
<booktitle>Linear and quasilinear equations of parabolic type</booktitle>
<publisher>Transl. Math. Monogr. Amer. Math. Soc. Providence, R.I., 23</publisher>
<year>1967</year>
<mr>MR0241822</mr>
</book>

<article>
<bibitem>8</bibitem>
<author>Oleinik, O. A.; Kalashnikov, A. A.; Chzou, Yui-Lin</author>
<title>The Cauchy problem and boundary problems for equations of the type of unsteady filtrations</title>
<journal>Izv. Akad. Nauk SSSR, Ser. Math.</journal>
<vol>22</vol>
<year>1958</year>
<page>667-704</page>
<mr>MR0099834</mr>
</article>

<article>
<bibitem>9</bibitem>
<author>Sabinina, E. S.</author>
<title>On the Cauchy problem for the equation of nonstationary gas filtration in several space variables</title>
<journal>Soviet Math.</journal>
<vol>2</vol>
<year>1961</year>
<page>166-199</page>
<mr>MR0158190</mr>
</article>

</references>
</top_article>
