arXiv subjects

David Winterrose

Publications and source records attributed to David Winterrose.

2 recordsLinked to original sources

arXiv2019

On the transfer of information in multiplier equations

We derive spectral width estimates for traces of tempered solutions of a large class of multiplier equations in $\mathbf{R}^n$. The estimates are uniform for solutions up to a given order. In the process, we find a rather explicit expression for a tempered fundamental solution of a multiplier. We successfully verify our spectral width estimates against numerical results in several scenarios involving the inhomogeneous Helmholtz equation in $\mathbf{R}^n$ with $n=1,\dots,9$. Our main result is directly applicable in the stability analysis of solutions of inverse source problems.

math.AP↗

arXiv2019

Variable exponent Calderón's problem in one dimension

We consider one-dimensional Calderón's problem for the variable exponent $p(\cdot)$-Laplace equation and find out that more can be seen than in the constant exponent case. The problem is to recover an unknown weight (conductivity) in the weighted $p(\cdot)$-Laplace equation from Dirichlet and Neumann data of solutions. We give a constructive and local uniqueness proof for conductivities in $L^\infty$ restricted to the coarsest sigma-algebra that makes the exponent $p(\cdot)$ measurable.

math.AP↗