Related papers: Calderon-Zygmund estimates for generalized double …
Global weighted $L^{p}$-estimates are obtained for the gradient of solutions to a class of linear singular, degenerate elliptic Dirichlet boundary value problems over a bounded non-smooth domain. The coefficient matrix is symmetric,…
We introduce a new sparse $T1$ theorem that estimates the dual pair associated with a Calderon-Zygmund operator by a sub-bilinear form supported on a sparse family of cubes. The main result in the paper improves previous sparse $T1$…
Global and local weighted Gagliardo-Nirenberg inequalities with doubling measures are established. These inequalities are key ingredients for the regularity theory and existence of strong solutions for strongly coupled parabolic and…
The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…
We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded…
In this note, we give a simple proof of the pointwise BMO estimate for Poisson's equation. Then the Calder\'{o}n-Zygmund estimate follows by the interpolation and duality.
In this paper, the aim of our work is to establish global weighted gradient estimates via fractional maximal functions and the point-wise regularity estimates of Dirichlet problem for divergence elliptic equations of the type \begin{align*}…
In this paper we obtain Calder\'on-Zygmund estimates for the laplacian of the following fourth order quasilinear elliptic problem $$ \Delta(g(\Delta u)\Delta u) = \Delta(g(\Delta f)\Delta f). $$ where the primitive of $g(t)t$, $G(t)$, is an…
In this work, we introduce two novel classes of quasilinear elliptic equations, each driven by the double phase operator with variable exponents. The first class features a new double phase equation where exponents depend on the gradient of…
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…
We realize Derksen-Weyman-Zelevinsky's mutations of representations as densely-defined regular maps on representation spaces, and study the generic values of Caldero-Chapoton functions with coefficients, giving, for instance, a sufficient…
We prove weighted mixed-norm $L^q_t(W^{2,p}_x)$ and $L^q_t(C^{2,\alpha}_x)$ estimates for $1<p,q<\infty$ and $0<\alpha<1$, weighted mixed weak-type estimates for $q=1$, $L^\infty_{t}(L^p_x)-BMO_t(W^{2,p}_x)$, and…
In this paper we introduce a new class of quasilinear elliptic equations driven by the so-called double phase operator with variable exponents. We prove certain properties of the corresponding Musielak-Orlicz Sobolev spaces (an equivalent…
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…
Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence form over a Lipschitz domain $\Omega$. The gradient estimates…
Consider the second order divergence form elliptic operator $L$ with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calder\'{o}n-Zygmund theory.…
In this article, we study regularity properties for degenerate parabolic double-phase equations. We establish continuity estimates for bounded weak solutions in terms of elliptic Riesz potentials on the right-hand side of the equation.
We establish two-weight norm inequalities for singular integral operators defined on spaces of homogeneous type. We do so first when the weights satisfy a double bump condition and then when the weights satisfy separated logarithmic bump…
The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for…
Calibration weighting is a fundamental technique in survey sampling and data integration for incorporating auxiliary information and improving efficiency of estimators. Classical calibration methods are typically formulated through distance…