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Regularity for a Nonlinear Discontinuous Subelliptic System with Drift on the Heisenberg Group
Advances in Mathematical Physics, 2022 In this paper, we prove the partial Hölder regularity of weak solutions and the partial Morrey regularity to horizontal gradients of weak solutions to a nonlinear discontinuous subelliptic system with drift on the Heisenberg group by the A-harmonic ...
Junli Zhang, Jialin Wang
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Bounds of Riesz Transforms on $L^p$ Spaces for Second Order Elliptic Operators [PDF]
, 2004 For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.Comment: To appear in Annales de L ...
Shen, Zhongwei
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Regularity results for singular elliptic problems
Journal of Function Spaces and Applications, 2006 Some local and global regularity results for solutions of linear elliptic equations in weighted spaces are proved. Here the leading coefficients are VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a ...
Loredana Caso
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Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains [PDF]
, 2010 This is a survey of results mostly relating elliptic equations and systems of arbitrary even order with rough coefficients in Lipschitz graph domains.
Maz'ya, Vladimir, Shaposhnikova, Tatyana
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An existence result for elliptic equations with VMO-coefficients
Journal of Mathematical Analysis and Applications, 2007 The paper deals with existence and uniqueness of solutions to the Dirichlet problem \[ \begin{cases} u\in W^{2,p}(\Omega)\cap W^{1,p}_0(\Omega),\cr Lu=f\in L^p(\Omega), \end{cases} \] with unbounded domain \(\Omega\subset \mathbb R^n,\) \(n\geq3,\) for the linear uniformly elliptic operator \[ L=-\sum_{i,j=1}^n a_{ij}{{\partial^2}\over{\partial x_i ...
CASO, Loredana +2 more
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The Dirichlet Problem for elliptic equations in unbounded domains of the plane
Journal of Function Spaces and Applications, 2008 In this paper we prove a uniqueness and existence theorem for the Dirichlet problem in W2,p for second order linear elliptic equations in unbounded domains of the plane.
Paola Cavaliere, Maria Transirico
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Quasilinear elliptic equations with VMO coefficients [PDF]
Transactions of the American Mathematical Society, 1995 Strong solvability and uniqueness in Sobolev space W 2 , n ( Ω ) {W^{2,n}}(\Omega ) are proved for the Dirichlet problem \[ { u =
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Hydrogen Bond‐Assisted PCET and Formation of WIII─OH in Bis(Dithiolene) Complex
Angewandte Chemie, Volume 137, Issue 31, July 28, 2025.The single crystal structure of complex [2Et3NH‐1] reveals hydrogen bonding at both W‐oxo and dithiolene‐S sites within the bis(dithiolene) WIV‐oxo complex. This finding provides critical evidence for dithiolene's involvement in proton reactions in high‐valent W‐oxo complexes.
Wonjung Lee +9 more
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Partial regularity for parabolic systems with VMO-coefficients
Communications on Pure and Applied Analysis, 2021 The author studies the regularity properties of the solutions of the following parabolic system in divergence form \[ u_t-\mathrm{div} A(x,t,u,Du)=0 \qquad \text{ in } \Omega_T=\Omega\times(-T,0)) \] It is established a partial Hölder regularity result for the weak solutions imposing standard \(p\)-growth condition and ellipticity condition on the ...
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A comparison theorem for nonsmooth nonlinear operators
, 2019 We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearity $f$ is $L^p$ function with $p > 1$.
Kozlov, Vladimir, Nazarov, Alexander
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