This paper gives new existence results for elliptic and evolutionary variational and quasi-
variational inequalities. Specifically, we give an existence theorem for evolutionary …

We propose a regularization scheme for image reconstruction that leverages the power of
deep learning while hinging on classic sparsity-promoting models. Many deep-learning …

State-of-the-art image reconstruction often relies on complex, highly parameterized deep
architectures. We propose an alternative: a data-driven reconstruction method inspired by …

We consider solution-driven adaptive variants of Total Variation, in which the adaptivity is
introduced as a fixed point problem. We provide existence theory for such fixed points in the …

In this article we propose a new formulation of the equations of the humid atmosphere with a
multi-phase saturation generalizing thus the model studied in Temam and Wu (2015 J …

We introduce a new general TV regularizer, namely, generalized TV regularization, to study
image denoising and nonblind image deblurring problems. In order to discuss the …

Choices of regularization parameters are central to variational methods for image
restoration. In this paper, a spatially adaptive (or distributed) regularization scheme is …

We extend our study for the warm cloud model in [13] to the analysis of a more general cloud
model including the ice microphysics in [28]. The moisture variables comprise water vapor …

The goal of this thesis is to analyze from the mathematical viewpoint certain models arising
in geophysical fluid mechanics and climate dynamics. In particular, we consider the humid …

The mathematical equations of the humid atmosphere are a system of nonlinear partial
differential equations (PDEs) on the temperature T, vapor humidity q and the velocity field u …