Tagged Questions
2
votes
1answer
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question 9 - chap 5 evans PDE
The question is :
Integrate by parts to prove :
$$\int_{U} |Du|^p \ dx \leq C \left(\int_{U} |u|^p \ dx\right)^{1/2} \left(\int_{U} |D^2 u|^p \ dx\right)^{1/2}$$
for $ 2 \leq p < \infty$ ...
0
votes
1answer
79 views
Identifying inequalities for 3D region.
I am having some difficulty identifying the bounds of a three-dimensional region.
I am asked to evaluate $\iiint_R (xz+3z)dV$, where $R$ is the region bounded by the cylinder $x^2 + z^2 = 9$ and the ...
5
votes
1answer
378 views
Hölder inequality from Jensen inequality
I'm taking a course in Analysis in which the following exercise was given.
Exercise Let $(\Omega, \mathcal{F}, \mu)$ be a probability space. Let $f\ge 0$ be a measurable function.
Using Jensen's ...
