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The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables…

In this paper we develop a new approach to the calibration of polarimetric radar data based on two key ideas. The first is the use of in-scene trihedral corner reflectors not only for radiometric and geometric calibration but also to…

This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…

We obtain a global fractional Calder\'on-Zygmund regularity theory for the fractional Poisson problem. More precisely, for $\Omega \subset \mathbb{R}^N$, $N \geq 2$, a bounded domain with boundary $\partial \Omega$ of class $C^2$, $s \in…

On a Riemannian manifold we define a one-parameter family of Laplacians acting on sections of any bundle associated to the principal frame bundle via a representation, and show how various examples fit into this framework.

We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…

We introduce the concept of Calder\'on-Zygmund inequalities on Riemannian manifolds. For $1<p<\infty$, these are inequalities of the form $$ \left\Vert \mathrm{Hess}\left( u\right) \right\Vert _{L^p}\leq C_{1}\left\Vert u\right\Vert…

We find a spinorial representation of a Riemannian or Lorentzian surface in a Lorentzian homogeneous space of dimension $3.$ We in particular obtain a representation theorem for surfaces in the $\mathbb{L}(\kappa,\tau)$ spaces. We then…

We construct a Cauchy type formula on open subdomains of Riemann surfaces

This is the introductory part of my PhD thesis on inverse problems arising in medical and seismic imaging. The topics include X-ray tomography of scalar and vector fields with partial data, higher order fractional Calder\'on problems,…

The Calder\'on-Zygmund inequality is a cornerstone of harmonic analysis and partial differential equations. In this article, we establish various Calder\'on-Zygmund inequalities on evolving Riemannian manifolds with bounded curvature. We…

The study of the paper mainly focusses on recovering the dissipative parameter in a cascade system coupling a bilaplacian operator to a heat equation from final time measured data via quasi-solution based optimization. The coefficient…

Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…

We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal…

This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a…

In this article, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: \begin{eqnarray*} \left\{\begin{array}{l@{\quad }l} (-\Delta)^\alpha u=f(x,u,v,\nabla u, \nabla v) &{\rm…

In this paper we study a semilinear problem for the fractional laplacian that are the counterpart of the Neumann problems in the classical setting. We show uniqueness of minimal energy solutions for small domains.

For the scattering system given by the Laplacian in a half-space with a periodic boundary condition, we derive resolvent expansions at embedded thresholds, we prove the continuity of the scattering matrix, and we establish new formulas for…

We describe a simple way of constructing exponentially growing solutions of the second order systems with the Laplacian as the principal term.

We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogous to Bernstein's theorem on non-parametric minimal surfaces.…