Boundary partial Holder regularity for elliptic systems with non-standard growth
Electronic Journal of Differential Equations, 2018 We investigate regular points on the boundaries of elliptic systems with non-standard growth, in particular, so-called Orlicz growth. A regular point on the boundary in this paper is a point for which a weak solution to a system is Holder continuous ...
Jihoon Ok
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Dirichlet problem for general A-harmonic equations in simply connected domains
Доповiдi Нацiональної академiї наук УкраїниThe article is devoted to theorems on the existence, representation, and regularity of solutions to the Dirichlet problem with continuous data for general A-harmonic equation div A grad U = 0 in the real plane with matrix valued coefficients A.
В.Я. Гутлянський +3 more
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Parabolic equations with VMO coefficients in spaces with mixed norms [PDF]
, 2008 An $L_{q}(L_{p})$-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class $VMO_{x}$, which, in particular, contains all measurable functions depending only on $t$. The method of proving simplifies the methods previously used in the case $p=q$.
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Resolvent approaches to elliptic regularity in stationary Fokker–Planck equations
Demonstratio MathematicaThis paper investigates the local regularity of solutions to stationary Fokker–Planck equations on an open set U⊂Rd $U\subset {\mathbb{R}}^{d}$ with d ≥ 2.
Lee Haesung
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Electronic Journal of Differential Equations, 2018 We show continuity in generalized Orlicz-Morrey spaces $M_{\Phi,\varphi}(\mathbb{R}^n)$ of sublinear integral operators generated by Calderon-Zygmund operator and their commutators with BMO functions.
Vagif S. Guliyev +3 more
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On divergence form SPDEs with VMO coefficients in a half space
Stochastic Processes and their Applications, 2009 We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in divergence form in $\bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.
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Partial regularity for elliptic systems with VMO-coefficients
, 2013 We establish partial regularity for vector-valued solutions to inhomogeneous elliptic systems in divergence form where the coefficients are possibly discontinuous with respect to $x$. More precisely, we assume a VMO-condition with respect to the $x$ and continuity with respect to $u$ and prove Hölder continuity of the solutions outside of singular sets.
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On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients
, 2010 We prove the solvability in Sobolev spaces $W^{1,2}_p$, $p>d+1$, of the terminal-boundary value problem for a class of fully nonlinear parabolic equations, including parabolic Bellman's equations, in bounded cylindrical domains with VMO ``coefficients''.
Dong, Hongjie, Krylov, N. V., Li, Xu
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Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms
Journal of Functional Analysis, 2007 The author studies the Cauchy problem for second-order divergence and non-divergence type equations: \[ \begin{aligned} L u(t,x)&= u_t(t,x) +a^{ij}(t,x)u_{x^ix^j}(t,x)+ b^i(t,x)u_{x^i}(t,x)+c(t,x) u(t,x),\\ {\mathcal L } u(t,x)&= u_t(t,x) +\big(a^{ij}(t,x)u_{x^i}(t,x)+ \bar b^j(t,x)u(t,x)\big)u_{x^j} + b^i(t,x)u_{x^i}(t,x)+c(t,x) u(t,x) \end{aligned} \]
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Change of the cross-sectional area of vastus medialis oblique in patients with recurrent patellar dislocation treated by tibial tubercle transfer combined with medial patellofemoral ligament reconstruction on axial CT. [PDF]
J Orthop Surg Res, 2022 Zhao C +5 more
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