Pith. sign in

REVIEW 1 cited by

An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2112.08305 v1 pith:E5WYGXDG submitted 2021-12-15 math.AP math.DG

Ali Feizmohammadi , Tony Liimatainen , Yi-Hsuan Lin This is my paper
classification math.APmath.DG
keywords equationsemilinearellipticanisotropicconformallytransversallyanalyzingassociated
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Given a conformally transversally anisotropic manifold $(M,g)$, we consider the semilinear elliptic equation $$(-\Delta_{g}+V)u+qu^2=0\quad \text{on $M$}.$$ We show that an a priori unknown smooth function $q$ can be uniquely determined from the knowledge of the Dirichlet-to-Neumann map associated to the semilinear elliptic equation. This extends the previously known results of the works [FO20, LLLS21a]. Our proof is based on analyzing higher order linearizations of the semilinear equation with non-vanishing boundary traces and also the study of interactions of two or more products of the so-called Gaussian quasimode solutions to the linearized equation.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Partial data Calder\'{o}n problem for quasilinear conductivities in dimension 2

    math.AP 2026-07 conditional novelty 6.0 of 10

    Partial boundary measurements uniquely determine a quasilinear two-dimensional conductivity γ(x,u,∇u) without restricting the gradient dependence.

Pith tools