6533b85dfe1ef96bd12bdda2

RESEARCH PRODUCT

On some partial data Calderón type problems with mixed boundary conditions

Angkana RülandGiovanni CoviGiovanni Covi

subject

osittaisdifferentiaaliyhtälötinverse problemsApplied Mathematics(fractional) Calderón problem010102 general mathematicsDegenerate energy levelsMathematical analysisBoundary (topology)Duality (optimization)Type (model theory)partial dataCarleman estimates01 natural sciencesinversio-ongelmatrunge approximationcomplex geometrical optics solutions010101 applied mathematicsBounded functionBoundary value problemUniqueness0101 mathematicsapproksimointiAnalysisMathematicsestimointi

description

In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. The CGO solutions are constructed by duality to a new Carleman estimate. peerReviewed

yearjournalcountryeditionlanguage
2021-07-01Journal of Differential Equations
10.1016/j.jde.2021.04.004http://dx.doi.org/10.1016/j.jde.2021.04.004