arXiv subjects

David Johansson

Publications and source records attributed to David Johansson.

7 recordsLinked to original sources

arXiv2026

Reconstruction of non-self-adjoint anisotropic and complex inclusions in the Calder\'on problem

We generalize recent results on the monotonicity method, for inclusion detection in the partial data anisotropic Calder\'on problem, to very general non-self-adjoint perturbations. This involves a forward model that accounts for both the anisotropic real conductivity and the anisotropic permittivity, and the results hold in any spatial dimension $d \geq 2$. We assume that the inclusion boundaries can be reached from the domain boundary via a set on which the background conductivity is self-adjoint, and that a definiteness condition holds near the inclusion boundaries. Away from the inclusion boundaries we allow general $L^\infty$ non-self-adjoint perturbations. We only require unique continuation based on the self-adjoint part of the background conductivity, thus making the methods compatible with generic unique continuation results.

math.AP↗

arXiv2026

Recovery of nonlinear material parameters in a quasilinear Lam\'e system

We investigate the inverse problem of determining nonlinear elastic material parameters from boundary stress measurements corresponding to prescribed boundary displacements. The material law is described by a nonlinear, space-independent elastic tensor depending on both the displacement and the strain, and gives rise to a general class of quasilinear Lam\'e systems. We prove the unique and stable recovery of a wide class of space-independent nonlinear elastic tensors, including the identification of two nonlinear isotropic Lam\'e moduli as well as certain anisotropic tensors. The boundary measurements are assumed to be available at a finite number of boundary points and, in the isotropic case, at a single point. Moreover, the measurements are generated by boundary displacements belonging to an explicit class of affine functions. The analysis is based on structural properties of nonlinear Lam\'e systems, including asymptotic expansions of the boundary stress and tensorial calculus.

math.AP↗

arXiv2025

Direct reconstruction of anisotropic self-adjoint inclusions in the Calder\'on problem

We extend the monotonicity method for direct exact reconstruction of inclusions in the partial data Calder\'on problem, to the case of general anisotropic conductivities in any spatial dimension $d\geq 2$. From a local Neumann-to-Dirichlet map, we give reconstruction methods of inclusions based on unknown anisotropic self-adjoint perturbations to a known anisotropic conductivity coefficient. This additionally provides new insights into the non-uniqueness issues of the anisotropic Calder\'on problem. The main assumption is a definiteness condition for the perturbations near the outer inclusion boundaries. Beyond this condition, they are $L^\infty$-perturbations that may be indefinite away from the outer inclusion boundaries, and with no boundary regularity requirement for the inclusions. Alternatively, we allow extreme parts that are perfectly insulating or perfectly conducting, in which case we require Lipschitz regularity of the outer inclusion boundaries.

math.AP↗

arXiv2025

Grounded Gesture Generation: Language, Motion, and Space

Human motion generation has advanced rapidly in recent years, yet the critical problem of creating spatially grounded, context-aware gestures has been largely overlooked. Existing models typically specialize either in descriptive motion generation, such as locomotion and object interaction, or in isolated co-speech gesture synthesis aligned with utterance semantics. However, both lines of work often treat motion and environmental grounding separately, limiting advances toward embodied, communicative agents. To address this gap, our work introduces a multimodal dataset and framework for grounded gesture generation, combining two key resources: (1) a synthetic dataset of spatially grounded referential gestures, and (2) MM-Conv, a VR-based dataset capturing two-party dialogues. Together, they provide over 7.7 hours of synchronized motion, speech, and 3D scene information, standardized in the HumanML3D format. Our framework further connects to a physics-based simulator, enabling synthetic data generation and situated evaluation. By bridging gesture modeling and spatial grounding, our contribution establishes a foundation for advancing research in situated gesture generation and grounded multimodal interaction. Project page: https://groundedgestures.github.io/

cs.CV↗

arXiv2025

Inverse problems for semilinear elliptic equations with low regularity

We show that a general nonlinearity $a(x,u)$ is uniquely determined, possibly up to a gauge, in a neighborhood of a fixed solution from boundary measurements of the corresponding semilinear equation. The main theorems are low regularity counterparts of the results in our recent paper (Johansson, Nurminen, Salo; ArXiv preprint 2312.12196).

math.AP↗

arXiv2024

Corrosion detection by identification of a nonlinear Robin boundary condition

We study an inverse boundary value problem in corrosion detection. The model is based on a conductivity equation with nonlinear Robin boundary condition. We prove that the nonlinear Robin term can be identified locally from Cauchy data measurements on a subset of the boundary. A possible strategy for turning a local identification result into a global one is suggested, and a partial result is proved in this direction. The inversion method is an adaptation to this nonlinear Robin problem of a method originally developed for semilinear elliptic equations. The strategy is based on linearization and relies on parametrizing solutions of the nonlinear equation on solutions of the linearized equation.

math.AP↗

arXiv2023

Inverse problems for semilinear elliptic PDE with a general nonlinearity $a(x,u)$

This article studies the inverse problem of recovering a nonlinearity in an elliptic equation $\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first order linearization achieve this under a sign condition on $\partial_u a(x,u)$, and results based on higher order linearization recover the Taylor series of $a(x,u)$ with respect to $u$. We improve these results and show that a general nonlinearity, and not just its Taylor series, is uniquely determined up to gauge near a fixed solution. Our method is based on constructing a good solution map that locally parametrizes solutions of the nonlinear equation by solutions of the linearized equation.

math.AP↗