The fractional -biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems

M Kar, J Railo, P Zimmermann - Calculus of Variations and Partial …, 2023 - Springer
This article investigates nonlocal, quasilinear generalizations of the classical biharmonic
operator (-Δ) 2. These fractional p-biharmonic operators appear naturally in the variational …

Recovery of coefficients for a weighted p-Laplacian perturbed by a linear second order term

CI Cârstea, M Kar - Inverse Problems, 2020 - iopscience.iop.org
This paper considers the inverse boundary value problem for the equation∇⋅(σ∇ u+ a|∇ u|
p− 2∇ u)= 0. We give a procedure for the recovery of the coefficients σ and a from the …

Inverse transport and diffusion problems in photoacoustic imaging with nonlinear absorption

RY Lai, K Ren, T Zhou - SIAM Journal on Applied Mathematics, 2022 - SIAM
Motivated by applications in imaging nonlinear optical absorption by photoacoustic
tomography, we study in this work inverse coefficient problems for a semilinear radiative …

Inverse problems for a class of elliptic obstacle problems involving multivalued convection term and weighted -Laplacian

S Zeng, S Migórski, AA Khan, JC Yao - Optimization, 2023 - Taylor & Francis
In this paper, we study the inverse problem of estimating discontinuous parameters and
boundary data in a nonlinear elliptic obstacle problem involving a nonhomogeneous …

Prescribed nonlinearity helps in an anisotropic Calder\'on-type problem

CI Cârstea - arXiv preprint arXiv:2406.14970, 2024 - arxiv.org
In this paper I consider the inverse boundary value problem for a quasilinear, anisotropic,
elliptic equation of the form $\nabla\cdot (\gamma\nabla u+|\nabla u|^{p-2}\nabla u)= 0 …

Variable exponent Calder\'on's problem in one dimension

T Brander, D Winterrose - arXiv preprint arXiv:1808.04168, 2018 - arxiv.org
We consider one-dimensional Calder\'on's problem for the variable exponent $ p (\cdot) $-
Laplace equation and find out that more can be seen than in the constant exponent case …

[PDF][PDF] Inverse problems for anisotropic obstacle problems with multivalued convection and unbalanced growth.

S Zeng, Y Bai, VD Rădulescu - Evolution Equations & Control Theory, 2023 - math.ucv.ro
The prime goal of this paper is to introduce and study a highly nonlinear inverse problem of
identification discontinuous parameters (in the domain) and boundary data in a nonlinear …

Boundary determination of coefficients appearing in a perturbed weighted -Laplace equation

N Kumar, T Sarkar, M Vashisth - arXiv preprint arXiv:2401.05980, 2024 - arxiv.org
We study an inverse boundary value problem associated with $ p $-Laplacian which is
further perturbed by a linear second order term, defined on a bounded set $\Omega $ in …

Recovering a variable exponent

T Brander, J Siltakoski - 2021 - content.ems.press
We consider an inverse problem of recovering the nonlinearity in the one dimensional
variable exponent p (x)-Laplace equation from the Dirichlet-to-Neumann map. The variable …