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inegalitatea gradienti in W_0^{1, p}(\Omega)

 
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Cezar Lupu
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PostPosted: Thu Mar 18, 2010 7:26 pm    Post subject: inegalitatea gradienti in W_0^{1, p}(\Omega) Reply with quote

Fie u, v\in W_{0}^{1, p}(\Omega), unde \Omega\subset\mathbb{R}^{N} este o submultime deschisa, nevida si marginita. Sa se arate ca, daca p\geq 2, atunci avem

\left|\nabla\left(\left(\frac{u^p+v^p}{2}\right)^{1/p}\right)\right| ^p\leq\frac{1}{2}|\nabla u|^p+\frac{1}{2}|\nabla v|^p.
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