Dirichlet boundary value problems for uniformly elliptic equations in modified local generalized Sobolev–Morrey spaces

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

doi:10.14232/ejqtde.2017.1.71

Cited by 12 publications

(12 citation statements)

References 29 publications

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“…The results presented here are a natural extension of the previous paper [7] to parabolic equations. Here we study the boundedness of the sublinear operators, generated by Calderon-Zygmund operators in generalized Morrey spaces and the regularity of the solutions of higher order uniformly elliptic boundary value problem in local generalized Morrey spaces where domain is bounded.…”

Section: Introductionsupporting

confidence: 57%

“…where C is independent of x and r: Suppose that a ∈ BMO and let T a be a sublinear operator satisfying (7).…”

Section: Sublinear Operators Generated By Parabolic Singular Integralmentioning

confidence: 99%

“…, let φ x 0 , r ðÞ be a weight function satisfying (20) and T a be a sublinear operator satisfying (7), (8). Then sublinear operator T a is bounded in M p,φ D nþ1 þ ÀÁ and…”

Section: Non-singular Integrals In Generalized Morrey Spacesmentioning

confidence: 99%

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The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains

Gadjiev¹,

Suleymanova²

2021

Recent Developments in the Solution of Nonlinear Differential Equations

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We study the regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations of higher order with vanishing mean oscillation (VMO) coefficients. We prove continuity in generalized parabolic Morrey spaces Mp,φ of sublinear operators generated by the parabolic Calderon-Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. We obtain strong solution belongs to the generalized Sobolev-Morrey space Wp,φm,1∘Q. Also we consider elliptic equation in unbounded domains.

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Section: Introductionsupporting

confidence: 57%

“…where C is independent of x and r: Suppose that a ∈ BMO and let T a be a sublinear operator satisfying (7).…”

Section: Sublinear Operators Generated By Parabolic Singular Integralmentioning

confidence: 99%

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The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains

Gadjiev¹,

Suleymanova²

2021

Recent Developments in the Solution of Nonlinear Differential Equations

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“…p,ϕ (H n ) is the generalized Morrey space M p,ϕ (H n ) studied by Guliyev et al [20], and LM α,V p,ϕ (H n ) is the central generalized Morrey space LM p,ϕ (H n ) studied by first author in [14]; see also [10,15,17,19,21,23,34,35]…”

Section: Definition 11 Let ϕ(R) Be a Positive Measurable Function Onmentioning

confidence: 99%

Morrey-type estimates for commutator of fractional integral associated with Schrödinger operators on the Heisenberg group

2018

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Let L =-H n + V be a Schrödinger operator on the Heisenberg group H n , where the nonnegative potential V belongs to the reverse Hölder class RH q 1 for some q 1 ≥ Q/2, and Q is the homogeneous dimension of H n. Let b belong to a new Campanato space θ ν (ρ), and let I L β be the fractional integral operator associated with L. In this paper, we study the boundedness of the commutators [b, I L β ] with b ∈ θ ν (ρ) on central generalized Morrey spaces LM α,V p,ϕ (H n), generalized Morrey spaces M α,V p,ϕ (H n), and vanishing generalized Morrey spaces VM α,V p,ϕ (H n) associated with Schrödinger operator, respectively. When b belongs to θ ν (ρ) with θ > 0, 0 < ν < 1 and (ϕ 1 , ϕ 2) satisfies some conditions, we show that the commutator operator [b, I L β ] is bounded from LM α,V p,ϕ 1 (H n) to LM α,V q,ϕ 2 (H n), from M α,V p,ϕ 1 (H n) to M α,V q,ϕ 2 (H n), and from VM α,V p,ϕ 1 (H n) to VM α,V q,ϕ 2 (H n), 1/p-1/q = (β + ν)/Q.

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“…(i) When α = 0, and ϕ(r) = r (λ−Q)/p , M α,V p,ϕ (R n ) is the classical Morrey space M p,λ (R n ) introduced by Morrey in [24] and LM α,V p,ϕ (R n ) is the central Morrey space LM p,λ (R n ) studied by Alvarez et al in [3] on the Euclidean setting; [15,16,19,22]; (iv) M α,V p,ϕ (R n ) and LM α,V p,ϕ (R n ) are the generalized Morrey space and the central generalized Morrey space associated with Schrödinger operator, respectively, studied by Guliyev in [14] on the Euclidean setting, see also [1,2,20].…”

Section: Introductionmentioning

confidence: 99%

Fractional integral associated to Schrödinger operator on the Heisenberg groups in central generalized Morrey spaces

Eroğlu¹,

Gadjiev²,

Намазов³

2018

J. Nonlinear Sci. Appl.

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Dirichlet boundary value problems for uniformly elliptic equations in modified local generalized Sobolev–Morrey spaces

Cited by 12 publications

References 29 publications

The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains

The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains

Morrey-type estimates for commutator of fractional integral associated with Schrödinger operators on the Heisenberg group

Fractional integral associated to Schrödinger operator on the Heisenberg groups in central generalized Morrey spaces

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