<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f3.xsl"?>
<top_article>
 <mrnumber>MR1795972</mrnumber>
 <author>Kawohl, Bernhard and Kutev, Nikolay</author>
 <author_utf8>Bernhard KAWOHL and Nikolay KUTEV</author_utf8>
 <title>Comparison principle and Lipschitz regularity for viscosity               solutions of some classes of nonlinear partial differential               equations</title>
 <journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
 <volume>43</volume>
 <year>2000</year>
 <page>241--253</page>
 <url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/vol43/fe43-2-3.pdf</url_pdf>
 <url_infty_pdf>http://fe.math.kobe-u.ac.jp/FE/no-infty-pdf.pdf</url_infty_pdf>
 <mathsci_link> http://www.ams.org/mathscinet-getitem?mr=MR1795972</mathsci_link>
<fesi_info>
  <FILE>43-241</FILE>
  <YEAR>2000</YEAR>
  <TITLE>Comparison Principle and Lipschitz Regularity for Viscosity Solutions of Some Classes of Nonlinear Partial Differential Equations</TITLE>
  <AUTHOR>Bernhard KAWOHL and Nikolay KUTEV</AUTHOR>
  <AUTHOR_utf8>Bernhard KAWOHL and Nikolay KUTEV</AUTHOR_utf8>
</fesi_info>

<references>

<article>
<bibitem>1</bibitem>
<author>Alt, H. W.; Luckhaus, S.</author>
<title>Quasilinear elliptic-parabolic differential equations</title>
<journal>Math. Z.</journal>
<vol>183</vol>
<year>1983</year>
<page>311-341</page>
<mr>MR0706391</mr>
</article>

<article>
<bibitem>2</bibitem>
<author>Angenent, S.; Fila, M.</author>
<title>Interior gradient blow-up in a semilinear parabolic equation</title>
<journal>Diff. Int. Eq.</journal>
<vol>9</vol>
<year>1996</year>
<page>865-877</page>
<mr>MR1392084</mr>
</article>

<article>
<bibitem>3</bibitem>
<author>Barles, G.</author>
<title>A weak Bernstein method for non-linear elliptic equations</title>
<journal>Diff. Int. Eq.</journal>
<vol>4</vol>
<year>1991</year>
<page>241-262</page>
<mr>MR1081182</mr>
</article>

<article>
<bibitem>4</bibitem>
<author>Barles, G.; Diaz, G.; Diaz, J. I.</author>
<title>Uniqueness and continuum of foliated solutions for a quasilinear elliptic equation with a nonlipschitz nonlinearity</title>
<journal>Comm. Partial Differential Equations</journal>
<vol>17</vol>
<year>1992</year>
<page>1037-1050</page>
<mr>MR1177305</mr>
</article>

<article>
<bibitem>5</bibitem>
<author>Barles, G.; Murat, F.</author>
<title>Uniqueness and maximum principle for quasilinear elliptic equations with quadratic growth conditions</title>
<journal>Arch. Rational Mech. Anal.</journal>
<vol>133</vol>
<year>1995</year>
<page>77-101</page>
<mr>MR1367357</mr>
</article>

<article>
<bibitem>6</bibitem>
<author>Chen, Y.-G.; Giga, Y.; Goto, S.</author>
<title>Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations</title>
<journal>J. Differential Geom.</journal>
<vol>333</vol>
<year>1991</year>
<page>749-786</page>
<mr>MR1100211</mr>
</article>

<article>
<bibitem>7</bibitem>
<author>Crandall, M.; Ishii, H.; Lions, P.-L.</author>
<title>User's guide to viscosity solutions of second order partial differential equations</title>
<journal>Bull. Amer. Math. Soc.</journal>
<vol>27</vol>
<year>1992</year>
<page>1-67</page>
<mr>MR1118699</mr>
</article>

<article>
<bibitem>8</bibitem>
<author>Crandall, M.; Huan, Zhonghan</author>
<title>Nonuniqueness of viscosity solutions</title>
<journal>Differ. Int. Equations</journal>
<vol>5</vol>
<year>1992</year>
<page>1247-1265</page>
<mr>MR1184025</mr>
</article>

<article>
<bibitem>9</bibitem>
<author>Evans, L. C.; Spruck, J.</author>
<title>Motion of level sets by mean curvature I</title>
<journal>J. Differential Geom.</journal>
<vol>33</vol>
<year>1991</year>
<page>635-681</page>
<mr>MR1100206</mr>
</article>

<article>
<bibitem>10</bibitem>
<author>Fila, M.; Lieberman, G.</author>
<title>Derivative blow up and beyond for quasilinear parabolic equations</title>
<journal>Differ. Integral Eqs.</journal>
<vol>7</vol>
<year>1994</year>
<page>811-821</page>
<mr>MR1270105</mr>
</article>

<article>
<bibitem>11</bibitem>
<author>Giga, Y.</author>
<title>Interior derivative blow-up for quasilinear parabolic equations</title>
<journal>Discrete and Continuous Dynamical systems</journal>
<vol>1</vol>
<year>1995</year>
<page>449-461</page>
<mr>MR1355884</mr>
</article>

<article>
<bibitem>12</bibitem>
<author>Giga, Y.; Goto, S.; Ishii, H.; Sato, M.-H.</author>
<title>Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains</title>
<journal>Indiana Univ. Math. J.</journal>
<vol>40</vol>
<year>1991</year>
<page>443-470</page>
<mr>MR1119185</mr>
</article>

<book>
<bibitem>13</bibitem>
<author>Gilbarg, D.; Trudinger, N.</author>
<booktitle>Elliptic partial Differential Equations of Second order, 2nd edition</booktitle>
<publisher>Springer, Berlin</publisher>
<year>1983</year>
<mr>MR0737190</mr>
</book>

<book>
<bibitem>14</bibitem>
<author>Giusti, E.</author>
<booktitle>Minimal surfaces and functions of bounded variation</booktitle>
<publisher>Birkh&#228;user, Basel</publisher>
<year>1984</year>
<mr>MR0775682</mr>
</book>

<article>
<bibitem>15</bibitem>
<author>Huisken, G.</author>
<title>Nonparametric mean curvature evolution with boundary conditions</title>
<journal>J. Differential Equations</journal>
<vol>77</vol>
<year>1989</year>
<page>369-378</page>
<mr>MR0983300</mr>
</article>

<article>
<bibitem>16</bibitem>
<author>Ishii, H.</author>
<title>On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's</title>
<journal>Comm. Pure Appl. Math.</journal>
<vol>42</vol>
<year>1989</year>
<page>14-45</page>
<mr>MR0973743</mr>
</article>

<article>
<bibitem>17</bibitem>
<author>Ishii, H.</author>
<title>Perron's method for Hamilton-Jacobi equations</title>
<journal>Duke Math. J.</journal>
<vol>55</vol>
<year>1987</year>
<page>369-384</page>
<mr>MR0894587</mr>
</article>

<article>
<bibitem>18</bibitem>
<author>Ishii, H.; Ramaswamy, M.</author>
<title>Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients</title>
<journal>Comm. Partial Differential Equations</journal>
<vol>20</vol>
<year>1995</year>
<page>2187-2213</page>
<mr>MR1361736</mr>
</article>

<article>
<bibitem>19</bibitem>
<author>Ishii, H.; Souganidis, P. E.</author>
<title>Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor</title>
<journal>Tohoku Math. J.</journal>
<vol>47</vol>
<year>1995</year>
<page>227-250</page>
<mr>MR1329522</mr>
</article>

<article>
<bibitem>20</bibitem>
<author>Jensen, R.</author>
<title>The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations</title>
<journal>Arch. Rational Mech. Anal.</journal>
<vol>101</vol>
<year>1988</year>
<page>1-27</page>
<mr>MR0920674</mr>
</article>

<article>
<bibitem>21</bibitem>
<author>Kawohl, B.; Kutev, N.</author>
<title>Global behaviour of solutions to a parabolic mean curvature equation</title>
<journal>Differ. Integral Eqs.</journal>
<vol>8</vol>
<year>1995</year>
<page>1923-1946</page>
<mr>MR1348958</mr>
</article>

<article>
<bibitem>22</bibitem>
<author>Kawohl, B.; Kutev, N.</author>
<title>Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations</title>
<journal>Archiv der Mathematik</journal>
<vol>70</vol>
<year>1998</year>
<page>470-478</page>
<mr>MR1621990</mr>
</article>

<book>
<bibitem>23</bibitem>
<author>Kozdova, L. A.</author>
<booktitle>Methods of solving nonlinear problems in heat conduction</booktitle>
<publisher>Nauka, Moscow</publisher>
<year>1975 (in Russian)</year>
</book>

<book>
<bibitem>24</bibitem>
<author>Middleman, S.</author>
<booktitle>Transport phenomena in the cardiovascular system</booktitle>
<publisher>Wiley Interscience, New York</publisher>
<year>1972</year>
</book>

<article>
<bibitem>25</bibitem>
<author>Ohnuma, M.; Sato, K.</author>
<title>Singular degenerate parabolic equations with applications to the $p$-Laplace diffusion equation</title>
<journal>Comm. Partial Differential Equations</journal>
<vol>22</vol>
<year>1997</year>
<page>381-411</page>
<mr>MR1443043</mr>
</article>

<article>
<bibitem>26</bibitem>
<author>Oliker, V.; Uraltseva, N.</author>
<title>Evolution of nonparametric surfaces with speed depending on curvature II. The mean curvature case</title>
<journal>Comm. Pure Appl. Math.</journal>
<vol>46</vol>
<year>1993</year>
<page>97-135</page>
<mr>MR1193345</mr>
</article>

<book>
<bibitem>27</bibitem>
<author>Schlichting, H.</author>
<booktitle>Boundary-layer theory</booktitle>
<publisher>Mc Graw Hill, New York</publisher>
<year>1979</year>
<mr>MR0076530</mr>
</book>

<article>
<bibitem>28</bibitem>
<author>Trudinger, N.</author>
<title>H&#246;1der gradient estimates for fully nonlinear elliptic equations</title>
<journal>Proc. Royal Soc. Edinburgh A</journal>
<vol>108</vol>
<year>1988</year>
<page>57-65</page>
<mr>MR0931007</mr>
</article>

<article>
<bibitem>29</bibitem>
<author>Trudinger, N.</author>
<title>On regularity and existence of viscosity solutions of nonlinear second order, elliptic equations</title>
<journal>Partial Diff. Eq. and Calculus of Variations, vol. II, Eds. F. Colombini, A. Marino, L. Modica, S. Spagnolo, Birkh&#228;user, Boston</journal>
<year>1989</year>
<page>939-957</page>
<mr>MR1034037</mr>
</article>

<article>
<bibitem>30</bibitem>
<author>Trudinger, N.</author>
<title>Comparison principles and pointwise estimates for viscosity solutions</title>
<journal>Rev. Mat. Iberoamericana</journal>
<vol>4</vol>
<year>1988</year>
<page>453-468</page>
<mr>MR1048584</mr>
</article>

</references>
</top_article>
