2025/01/03 by R. M. Brown, Russell M. Brown, D Faraco +6
Mathematics · Engineering · #Differential Equations and Boundary Problems #Elasticity and Wave Propagation #Material Science and Thermodynamics
paper · pdf · doi:10.1088/1361-6420/ae73ac
Abstract We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> </mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mtext>⩾</mml:mtext> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . We show that the map from the coefficients to a certain bilinear form is injective. We have a particular focus on obtaining these results under lower regularity on the coefficients. It is known that knowledge of this bilinear form is equivalent to a knowledge of a Dirichlet to Neumann map or the Cauchy data for solutions.