Morrey estimates for a class of elliptic equations with drift term

Abstract We consider the following boundary value problem $$\begin{array}{} \displaystyle \begin{cases} - {\rm div}{[M(x)\nabla u - E(x) u]} =f(x) & \text{in}~~ {\it\Omega} \\ u =0 & \text{on}~~ \partial{\it\Omega}, \end{cases} \end{array}$$ where Ω is a bounded open subset of ℝN, with N > 2, M : Ω → ℝN2 is a symmetric matrix, E(x) and f(x) are respectively a vector field and function both belonging to suitable Morrey spaces and we study the corresponding regularity of u and D u.

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Local regularity results for solutions of linear elliptic equations with drift term

Advances in Calculus of Variations ◽

10.1515/acv-2019-0048 ◽

2019 ◽

Vol 0 (0) ◽

Cited By ~ 1

Author(s):

G. R. Cirmi ◽

S. D’Asero ◽

Salvatore Leonardi ◽

Michaela M. Porzio

Keyword(s):

Boundary Value Problem ◽

Open Subset ◽

Elliptic Equations ◽

Vector Fields ◽

Nonlinear Boundary ◽

Divergence Form ◽

Local Regularity ◽

Drift Term ◽

Bounded Open Subset ◽

Regularity Results

Abstract We study the local regularity of the solution u of the following nonlinear boundary value problem: \left\{\begin{aligned} \displaystyle\mathcal{A}u&\displaystyle=-\operatorname{% div}{[E(x)u+F(x)]}&&\displaystyle\phantom{}\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{on }\partial% \Omega,\end{aligned}\right. where Ω is a bounded open subset of {\mathbb{R}^{N}} , with {N>2} , {\mathcal{A}} is a nonlinear Leray–Lions operator in divergence form, and {E(x)} and {F(x)} are vector fields satisfying suitable local summability properties.

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The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2020.57.1.1449 ◽

2020 ◽

Vol 57 (1) ◽

pp. 68-90 ◽

Cited By ~ 1

Author(s):

Tahir S. Gadjiev ◽

Vagif S. Guliyev ◽

Konul G. Suleymanova

Keyword(s):

Elliptic Equations ◽

A Priori Estimates ◽

A Priori ◽

Morrey Spaces ◽

Smooth Bounded Domain ◽

Weighted Morrey Spaces ◽

Priori Estimates ◽

Muckenhoupt Class ◽

Morrey Estimates ◽

Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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A uniqueness result for some singular semilinear elliptic equations

Communications in Contemporary Mathematics ◽

10.1142/s0219199715500844 ◽

2016 ◽

Vol 18 (06) ◽

pp. 1550084 ◽

Cited By ~ 9

Author(s):

Annamaria Canino ◽

Berardino Sciunzi

Keyword(s):

Elliptic Equation ◽

Boundary Conditions ◽

Open Subset ◽

Elliptic Equations ◽

Dirichlet Boundary ◽

Semilinear Elliptic Equation ◽

Uniqueness Result ◽

Dirichlet Boundary Conditions ◽

Semilinear Elliptic ◽

Bounded Open Subset

Given [Formula: see text] a bounded open subset of [Formula: see text], we consider non-negative solutions to the singular semilinear elliptic equation [Formula: see text] in [Formula: see text], under zero Dirichlet boundary conditions. For [Formula: see text] and [Formula: see text], we prove that the solution is unique.

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Some Elliptic Problems With Degenerate Coercivity

Advanced Nonlinear Studies ◽

10.1515/ans-2006-0101 ◽

2006 ◽

Vol 6 (1) ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Lucio Boccardo

Keyword(s):

Open Subset ◽

Elliptic Equations ◽

Principal Part ◽

Existence Of Solutions ◽

Elliptic Problems ◽

Nonlinear Elliptic Equations ◽

Model Case ◽

Nonlinear Elliptic ◽

Degenerate Coercivity ◽

Bounded Open Subset

AbstractIn this paper we are interested in existence of solutions for some nonlinear elliptic equations with principal part having degenerate coercivity. The model case iswith Ω bounded open subset of ℝ

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Radially symmetric solutions of a class of singular elliptic equations

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500018101 ◽

1990 ◽

Vol 33 (2) ◽

pp. 169-180 ◽

Cited By ~ 15

Author(s):

Juan A. Gatica ◽

Gaston E. Hernandez ◽

P. Waltman

Keyword(s):

Boundary Value Problem ◽

Elliptic Equations ◽

Boundary Value ◽

Open Unit ◽

Open Unit Ball ◽

Singular Elliptic Equations ◽

Existence Of Positive Solutions ◽

Radially Symmetric Solutions ◽

Image Position ◽

Special Case

The boundary value problemis studied with a view to obtaining the existence of positive solutions in C1([0, 1])∩C2((0, 1)). The function f is assumed to be singular in the second variable, with the singularity modeled after the special case f(x, y) = a(x)y−p, p>0.This boundary value problem arises in the search of positive radially symmetric solutions towhere Ω is the open unit ball in ℝN, centered at the origin, Γ is its boundary and |x| is the Euclidean norm of x.

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