this is the complete problem
and i have a problem that is : i dont understand step 2: step 1:"shows that $m>-\infty$ i dont understand how to prove it ?
can someone help me please ?
thank you
2026-03-27 23:12:51.1774653171
Coercive problems
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Put $a=\|u\|\geq0$. Then by using $2Ca\leq a^2+C^2$, we have $$ I(u) \geq \frac {a^2}2 - Ca \geq \frac {a^2}2 - \frac12(a^2+C^2) = -\frac12 C^2, $$ fort any $u\in H^1_0(\Omega)$. So the infimum of $I(u)$ as $u$ varies in $H^1_0(\Omega)$ must be larger than $-C^2/2$.