Results 1 to 10 of about 74 (68)

The John–Nirenberg Inequality of BLO With Hausdorff Content

Journal of Function Spaces
MSC2020 Classification: 42B35, 28A12 ...
Chenglong Fang
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Local Well-Posedness for the Fourth-Order Schrödinger Equation With Quadratic Derivative Nonlinearities in Fourier–Lebesgue Spaces

Journal of Function Spaces
MSC2020 Classification: 35G25, 35Q55, 42B35 ...
Long Xiao, Ting Chen
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Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part

Advances in Nonlinear Analysis, 2022
Let n≥2n\ge 2 and Ω⊂Rn\Omega \subset {{\mathbb{R}}}^{n} be a bounded nontangentially accessible domain. In this article, the authors investigate (weighted) global gradient estimates for Dirichlet boundary value problems of second-order elliptic equations
Yang Sibei, Yang Dachun, Yuan Wen
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Weighted W1, p (·)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains

Advances in Nonlinear Analysis, 2021
Let w be a Muckenhoupt A2(ℝn) weight and Ω a bounded Reifenberg flat domain in ℝn. Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition.
Zhang Junqiang, Yang Dachun, Yang Sibei
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Reversed Stein–Weiss Inequalities with Poisson-Type Kernel and Qualitative Analysis of Extremal Functions

Advanced Nonlinear Studies, 2021
Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces

Advances in Nonlinear Analysis, 2020
It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators

Demonstratio Mathematica, 2023
Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process.
Alharthi Nadiyah Hussain, Atangana Abdon, Alkahtani Badr S.   +2 more
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Smoothness of solutions of a convolution equation of restricted type on the sphere

Forum of Mathematics, Sigma, 2021
Let $\mathbb {S}^{d-1}$ denote the unit sphere in Euclidean space $\mathbb {R}^d$, $d\geq 2$, equipped with surface measure $\sigma _{d-1}$. An instance of our main result concerns the regularity of solutions of the convolution equation $$\begin{align*}a\
Diogo Oliveira e Silva, René Quilodrán
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Bernstein inequalities via the heat semigroup

, 2019
Math. Ann. 382, 783–819 (2022)We extend the classical Bernstein inequality to a general setting including Schrödinger operators and divergence form elliptic operators on Riemannian manifolds or domains.
Imekraz, Rafik, Ouhabaz, El Maati
core   +3 more sources

Examples of non-Dini domains with large singular sets

Advanced Nonlinear Studies, 2023
Let uu be a nontrivial harmonic function in a domain D⊂RdD\subset {{\mathbb{R}}}^{d}, which vanishes on an open set of the boundary. In a recent article, we showed that if DD is a C1{C}^{1}-Dini domain, then, within the open set, the singular set of uu ...
Kenig Carlos, Zhao Zihui
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