Seminar in Numerical Analysis: Alexey Chernov (Universität Oldenburg)

On analytic and Gevrey class regularity for parametric elliptic eigenvalue problems (A. Chernov, T. Le)

We investigate a class of parametric elliptic eigenvalue problems where the coefficients (and hence the solution) may depend on a parameter y. Understanding the regularity of the solution as a function of y is important for construction of efficient numerical approximation schemes. Several approaches are available in the existing literature, e.g. the complex-analytic argument by Andreev and Schwab (2012) and the real-variable argument by Gilbert et al. (2019+). The latter proof strategy is more explicit, but, due to the nonlinear nature of the problem, leads to slightly suboptimal results. In this talk we close this gap and (as a by-product) extend the analysis to the more general class of coefficients.

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

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