Article Contents
Article Contents

# Variational source conditions for inverse Robin and flux problems by partial measurements

• * Corresponding author: Jun Zou

The first author is supported by National Natural Science Foundation of China (Nos. 11701205 and 11871240). The second author is supported by National Natural Science Foundation of China (No. 11871240), NSFC-RGC (China-Hong Kong, No. 11661161017) and self-determined research funds of CCNU from the colleges' basic research and operation of MOE (No. CCNU20TS003). The third author is supported by the German Research Foundation (DFG grants YO159/2-2 and YO159/4-1). The fourth author is supported by Hong Kong RGC grant (project 14306719) and the NSFC/Hong Kong RGC Joint Research Scheme 2016/17 (N_CUHK437/16)

• This work is devoted to the convergence analysis of the Tikhonov regularization for the inverse Robin and flux problems.Both inverse problems aim at recovering a respective physical quantity on an inaccessible part of the boundary through some measurement on a partial accessible boundary.The convergence and convergence rate in the desirable L2-norm are derived based on two new logarithmic type stabilities (only in some weak norms,e.g.,the negative Sobolev norms), which enable us to construct and rigorously verify the required variational source conditions.

Addendum: The abstract is added since it was missing when the article was published online. To reflect this addition an Addendum is published in this same IPI 16-2 April 2022 regular issue. We apologize for any inconvenience this may cause.

Mathematics Subject Classification: Primary: 35R35, 41A25; Secondary: 65M32.

 Citation:

• Figure 1.  An example of $\Omega$ in ${{\mathbb R}}^2$ and $\Gamma_a$ (resp. $\Gamma_b$) is an open part of $\Gamma_1$ (resp. $\Gamma_2$)

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