Uniqueness and global convergence for a discretized inverse coefficient problem

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We then demonstrate that this result can be used to prove uniqueness, stability and global convergence for an inverse coefficient problem with finitely many measurements. We consider the problem of determining an unknown inverse Robin transmission coefficient in an elliptic PDE. Using a relation to monotonicity and localized potentials techniques, we show that a piecewise-constant coefficient on an a-priori known partition with a-priori known bounds is uniquely determined by finitely many boundary measurements and that it can be uniquely and stably reconstructed by a globally convergent Newton iteration. We derive a constructive method to identify these boundary measurements, calculate the stability constant and give a numerical example.

For further information about the seminar, please visit this webpage.

Asymptotic expansion of low-energy excitations for weakly interacting bosons

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

We consider a system of N bosons in the mean-field scaling regime in an external trapping potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N. We show that the structure of the ground state and of the non-degenerate low-energy eigenstates is preserved by the dynamics if

the external trap is switched off. This talk is based on joint works with Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer (arXiv:1912.11004 and arXiv:2006.09825).

High-regularity Invariant Measures for 2d and 3d Euler Equations and Growth of the Sobolev Norms

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk, I will present some results obtained in this direction. We will construct invariant measures for the 2d Euler equation at high regularity ($H^s$, $s>2$) and prove that on the support of the measure, Sobolev norms do not grow faster than polynomially.

Refining the method allows to construct an invariant measure to the 3d Euler equations at high regularity ($H^s$, $s>7/2$) and thus construct

global dynamics on the support of the measure, exhibiting at most polynomial growth.

Finally, it time permits we will discuss the properties of the measures constructed. ]]>

TBA

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Optimal regularity for viscous Hamilton-Jacobi equations in Lebesgue spaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>