| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
I was able to achieve an important aim that I planned in this study at first. It is to provide a lower estimate of the sup-norm of the gradient of a function by using the logarithmic Sobolev inequality with index p which is equal to infinity. This estimate is applied to show the optimality of the decay rate of the sup-norm of the gradients to solutions of several Cauchy problems. This result has been published in an appropriate mathematical journal. On the other hand, through workshops, I let many researchers know widely about my complete proof of the logarithmic Sobolev inequality with index p which is greater than 1. The paper of this proof was published in the beginning of this study. In these senses, the result of this study was able to be accomplished in a satisfactory form.
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