Zobrazeno 1 - 10
of 123
pro vyhledávání: '"Tzou, Leo"'
In this paper we prove two results. The first shows that the Dirichlet-Neumann map of the operator $\Delta_g+q$ on a Riemannian surface can determine its topological, differential, and metric structure. Earlier work of this type assumes a priori that
Externí odkaz:
http://arxiv.org/abs/2406.16944
Autor:
Busch, Leonard, Tzou, Leo
We consider a partial data inverse problem with unbounded potentials. Rather than rely on functional analytic arguments or Carleman estimates, we construct an explicit Green's function with which we construct complex geometric optics (CGO) solutions
Externí odkaz:
http://arxiv.org/abs/2312.04983
In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if $\Sigma$ is a $2$-dimensional embedded minimal surface, then the knowledge of the Dirichlet
Externí odkaz:
http://arxiv.org/abs/2310.14268
We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal analysis of
Externí odkaz:
http://arxiv.org/abs/2310.06925
We develop a systematic approach for resolving the analytic wave front set for a class of integral geometry transforms appearing in various tomography problems. Combined with microlocal analytic continuation, this leads to uniqueness and support theo
Externí odkaz:
http://arxiv.org/abs/2306.05906
This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold $(M,g,\partial M)$ under the singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions on a small
Externí odkaz:
http://arxiv.org/abs/2306.00491
Autor:
Tzou, J. C., Tzou, Leo
The L\'evy flight foraging hypothesis asserts that biological organisms have evolved to employ (truncated) L\'evy flight searches due to such strategies being more efficient than those based on Brownian motion. However, we provide here a concrete two
Externí odkaz:
http://arxiv.org/abs/2302.13976
We give an analytic description for the infinitesimal generator constructed by Applebaum-Estrade for L\'evy flights on a broad class of closed Riemannian manifolds including all negatively-curved manifolds, the flat torus and the sphere. Various prop
Externí odkaz:
http://arxiv.org/abs/2211.13973
In this article, we study the narrow capture problem on a Riemannian 2-manifold. This involves the derivation of the mean first passage (sojourn) time of a surface-bound ion modelled as a Brownian particle. We use a layer potential argument in conjun
Externí odkaz:
http://arxiv.org/abs/2209.12425
Autor:
Salo, Mikko, Tzou, Leo
We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the Dirichlet-to-Neum
Externí odkaz:
http://arxiv.org/abs/2202.05290