Related papers: Optimal gradient estimates for multi-phase integra…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

In this work, we study the robust phase retrieval problem where the task is to recover an unknown signal $\theta^* \in \mathbb{R}^d$ in the presence of potentially arbitrarily corrupted magnitude-only linear measurements. We propose an…

We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable…

We obtain necessary optimality conditions for higher-order infinite horizon problems of the calculus of variations via discrete quantum operators.

We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex case. Additionally, we prove a priori interior gradient estimates for any constant phases.

In this paper we investigate the improved Caccioppoli inequality and the reverse H\"{o}lder inequality for gradients of weak solutions to nonhomogeneous parabolic systems whose coefficients can be split into a complex-valued and bounded…

In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…

We study sharp weighted Sobolev-type inequalities of the form \[ \int_{0}^{1}|u(x)|\rho(x) \diff x \leqslant \Lambda \Bigl(\int_{0}^{1}|u^{(k)}(x)|^2 \diff x\Bigr)^{1/2}, \qquad u\in H_0^k(0,1), \] where $\rho$ is a non-negative weight. We…

The main aim of this note is to prove sharp weighted integral Hardy inequality and conjugate integral Hardy inequality on homogeneous Lie groups with any quasi-norm for the range $1<p\leq q<\infty.$ We also calculate the precise value of…

The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…

We prove the self-improving property of very weak solutions to non-uniformly elliptic problems of double phase type in divergence form under sharp assumptions on the nonlinearity.

We prove global Schauder estimates for kinetic Kolmogorov equations with coefficients that are H\"older continuous in the spatial variables but only measurable in time. Compared to other available results in the literature, our estimates…

We prove several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequalities for higher order derivatives including both the…

We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…

The aim of this note is twofold. Firstly, we prove an abstract version of the Calder\'on transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an operation does…

We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…

For a continuous-time phase-type distribution, starting with its Laplace-Stieltjes transform, we obtain a necessary and sufficient condition for its minimal phase-type representation to have the same order as the algebraic degree of the…

We derive second order estimates for $\chi$-plurisubharmonic solutions of complex Hessian equations with right hand sides depending on gradients on compact Hermitian manifolds.

We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…