typos

Mathematics/5th/Introduction_to_nonlinear_elliptic_PDEs/Introduction_to_nonlinear_elliptic_PDEs.tex

@@ -1069,9 +1069,9 @@
   \begin{proof}
     From the superquadradicity condition, for $t>0$, the function $\abs{t}^{-p}F(x,t)$ is nondecreasing (the derivative is nonnegative). So, for $0\leq t\leq 1$ we have $F(x,t)\leq \abs{t}^p F(x,1)$. Similarly, for $-1\leq t\leq 0$ we have $F(x,t)\leq \abs{t}^p F(x,-1)$. Using the upper estimate we get, for $\abs{t}\geq 1$, $\abs{F(x,t)}\leq \overline{\overline{C}} \abs{t}^{p_1}$ and so
     $\abs{F(x,t)}\leq C'(\abs{t}^p+\abs{t}^{p_1})$ $\forall t$ (the positivity of $F(x,1)$ and $F(x,-1)$ follows from the third hypothesis on $f$). So:
-    $$
-      \int_\Omega \abs{F(x,u)}\leq C'\left(\norm{u}_{
-    $$
+    % $$
+    %   \int_\Omega \abs{F(x,u)}\leq C'\left(\norm{u}_{
+    % $$
   \end{proof}
 \end{multicols}
 \end{document}