Regularity in generalized Morrey spaces of solutions to higher order nondivergence elliptic equations with VMO coefficients

Gadjiev, Tahir; Galandarova, Shahla; Guliyev, Vagif S.

doi:10.14232/ejqtde.2019.1.55

Cited by 12 publications

(4 citation statements)

References 31 publications

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“…We apply these estimates to study the regularity of the solution of Dirichlet problem for linear elliptic partial differential equations (see [3,16,17,20]). The presented results are generalization of previous works [4,5,6,8,19].…”

Section: Introductionsupporting

confidence: 86%

The Dirichlet problem for the uniformly higher-order elliptic equations in generalized weighted Sobolev-Morrey spaces

Guliyev,

Gadjiev,

Serbetci

2019

Preprint

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Section: Introductionsupporting

confidence: 86%

The Dirichlet problem for the uniformly higher-order elliptic equations in generalized weighted Sobolev-Morrey spaces

Guliyev,

Gadjiev,

Serbetci

2019

Preprint

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“…Recently, in [5,27,28] the authors studied some regularity results for solutions of linear partial differential equations with discontinuous coefficients in nondivergence form.…”

Section: (): V-volmentioning

confidence: 99%

Regularity of solutions of elliptic equations in divergence form in modified local generalized Morrey spaces

et al. 2020

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Aim of this paper is to prove regularity results, in some Modified Local Generalized Morrey Spaces, for the first derivatives of the solutions of a divergence elliptic second order equation of the form $$\begin{aligned} \mathscr {L}u{:}{=}\sum _{i,j=1}^{n}\left( a_{ij}(x)u_{x_{i}}\right) _{x_{j}}=\nabla \cdot f,\qquad \hbox {for almost all }x\in \Omega \end{aligned}$$ L u : = ∑ i , j = 1 n a ij ( x ) u x i x j = ∇ · f , for almost all x ∈ Ω where the coefficients $$a_{ij}$$ a ij belong to the Central (that is, Local) Sarason class CVMO and f is assumed to be in some Modified Local Generalized Morrey Spaces $$\widetilde{LM}_{\{x_{0}\}}^{p,\varphi }$$ LM ~ { x 0 } p , φ . Heart of the paper is to use an explicit representation formula for the first derivatives of the solutions of the elliptic equation in divergence form, in terms of singular integral operators and commutators with Calderón–Zygmund kernels. Combining the representation formula with some Morrey-type estimates for each operator that appears in it, we derive several regularity results.

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“…For a survey on spectral theory of higher order elliptic operators, including some estimates for the corresponding kernels, we refer to [14]. We also consider analogously problems [21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

The mixed boundary value problems for uniformly elliptic equations in modified local generalized Sobolev-Morrey spaces

2024

TRANSACTIONS.(issue MECHANICS)

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We consider problems which arise as mathematical models of various applied problems, mechanics, physics and so on. By using these results we prove the solvability of the mixed boundary value problem for a polyharmonic equation in modified local generalized Sobolev-Morrey spaces. We obtain a priori estimates for the solutions of the mixed boundary value problems for the uniformly elliptic equations in modified local generalized Sobolev-Morrey spaces defined on bounded smooth domains.

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Regularity in generalized Morrey spaces of solutions to higher order nondivergence elliptic equations with VMO coefficients

Cited by 12 publications

References 31 publications

The Dirichlet problem for the uniformly higher-order elliptic equations in generalized weighted Sobolev-Morrey spaces

The Dirichlet problem for the uniformly higher-order elliptic equations in generalized weighted Sobolev-Morrey spaces

Regularity of solutions of elliptic equations in divergence form in modified local generalized Morrey spaces

The mixed boundary value problems for uniformly elliptic equations in modified local generalized Sobolev-Morrey spaces

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