# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/Omegatimes(0,T);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$ \Omega\times (0,T)$">|; 

$key = q/1-epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ 1 -\epsilon $">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ q$">|; 

$key = q/Lambda_q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ \Lambda_q$">|; 

$key = q/epsilon>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ \epsilon &gt;0$">|; 

$key = q/beta_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ \beta_0 &gt; 0$">|; 

$key = q/|{cdot}_*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ \Vert {\cdot}_* $">|; 

$key = q/|{q_1-q_2}_{H^{beta}(mathbb{R}^{n})}leqM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$ \Vert {q_1 -q_2 }_{H^{\beta}(\mathbb{R}^{n}) }\leq M$">|; 

$key = q/beta>beta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$ \beta
&gt;\beta_0$">|; 

$key = q/u(x,0)=u_t(x,0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ u(x,0)=u_t (x,0)=0$">|; 

$key = q/u_{tt}-Deltau+qu=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$ u_{tt} - \Delta u + qu = 0$">|; 

$key = q/1slash3-epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$ 1/3-\epsilon$">|; 

$key = q/displaystyle|{q_1-q_2}_{L^{infty}(Omega)}leqC|{Lambda_{q_1}-Lambda_{q_2}}_*^{1-epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle \Vert {q_1 - q_2}_{L^{\infty} (\Omega)} \leq C \Vert {\Lambda_{q_1}-
\Lambda_{q_2} }_* ^{ 1 - \epsilon}$">|; 

$key = q/displaystyle|{q_1-q_2}_{L^{infty}(Omega)}leqC|{Lambda_{q_1}-Lambda_{q_2}}_*^{1slash3-epsilon}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle \Vert {q_1 - q_2}_{L^{\infty} (\Omega)} \leq C \Vert {\Lambda_{q_1}-
\Lambda_{q_2} }_* ^{ 1/3 - \epsilon}.$">|; 

1;