Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems by Mourad Choulli

Author:Mourad Choulli
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(2.65)

Also, as a consequence of Proposition 2.28, there is such that

(2.66)

Estimate (2.65) in (2.66) leads

in this estimate yields, where ,

which, in combination with (2.64), implies

We take in this inequality in order to obtain

Since is bounded, we get

(2.67)

Here .

Let and substitute in (2.67), by t. Then

(2.68)

When , the equation has a unique solution in . This unique solution is denoted by . Therefore

Then in (2.68) yields

(2.69)

If ,

(2.70)

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