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We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and divergence terms. Our main interest is to provide graph and…

We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values…

In this paper we establish some companions of perturbed Ostrowski type integral inequalities for functions whose second derivatives are bounded. Some applications to composite quadrature rules, and to probability density functions are also…

In this article, we establish radial symmetry for positive weak solutions of a class of mixed local-nonlocal equations with possibly singular nonlinearity via the moving plane method. Furthermore, we provide a quantitative version of…

We study coercive inequalities in Orlicz spaces associated to the probability measures on finite and infinite dimensional spaces which tails decay slower than the Gaussian ones. We provide necessary and sufficient criteria for such…

In this paper, we consider non-homogeneous fractional equations in Orlicz spaces, with a source depending on the spatial variable, the unknown function, and its fractional gradient. The latter is adapted to the Orlicz framework. The main…

This work is concerned with the quantification of the epistemic uncertainties induced the discretization of partial differential equations. Following the paradigm of probabilistic numerics, we quantify this uncertainty probabilistically.…

A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…

In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.

We prove the equivalence of two seemingly very different ways of generalising Rademacher's theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of…

General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…

We establish weighted Bernstein inequalities in $L^p$ space for the doubling weight on the conic surface $\mathbb{V}_0^{d+1} = \{(x,t): \|x\| = t, x \in \mathbb{R}^d, t\in [0,1]\}$ as well as on the solid cone bounded by the conic surface…

Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein distance in image processing and machine learning. However,…

In this paper we discuss some of the recent developments on derived equivalences in algebraic geometry.

In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…

We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These…

This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.

We prove a new Bernstein type inequality in $L^p$ spaces associated with the tangential derivatives on the boundary of a general compact $C^2$-domain. We give two applications: Marcinkiewicz type inequality for discretization of $L^p$ norm…

This note presents three resonances in commutative algebra and analytic geometry of the concept of Lojasiewicz inequality. The first is the interpretation in complex analytic geometry of the best possible exponent for a function g with…

In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.