Niky Kamran (University Â鶹´«Ã½ÍøÕ¾)
Title:Â Logarithmic stability in the inverse Steklov problem on warped products.
´¡²ú²õ³Ù°ù²¹³¦³Ù:ÌýWe study the amount of information contained in the Steklov spectrum of some compact manifolds with connected boundary equipped with a warped product metric. Examples of such manifolds include deformed balls in R^d. We first show that the Steklov spectrum determines uniquely the warping function and also show that the approximate knowledge (in a given technical sense) of the Steklov spectrum is enough to determine uniquely the warping function in a neighbourhood of the boundary. Second, we provide logarithmic stability estimates on the warping function from the Steklov spectrum. The key element of these stability results relies on a formula that, roughly speaking, connects the inverse data (the Steklov spectrum) to the Laplace transform of the difference of the two warping factors.
Location: Room PK-5115, Président-Kennedy Building, UQAM.