• Corpus ID: 245853772

Note on Green's functions of non-divergence elliptic operators with continuous coefficients

@inproceedings{Dong2022NoteOG,
  title={Note on Green's functions of non-divergence elliptic operators with continuous coefficients},
  author={Hongjie Dong and Seick Kim and Sungjin Lee},
  year={2022}
}
We improve a result in Kim and Lee (Ann. Appl. Math. 37(2):111–130, 2021): showing that if the coefficients of an elliptic operator in non-divergence form are of Dini mean oscillation, then its Green’s function has the same asymptotic behavior near the pole x0 as that of the corresponding Green’s function for the elliptic equation with constant coefficients frozen at x0 . 
1 Citations

The Fundamental Solution of an Elliptic Equation with Singular Drift

. For n ≥ 3, we study the existence and asymptotic properties of the fundamental solution for elliptic operators in nondivergence form, L ( x,∂ x ) = a ij ( x ) ∂ i ∂ j + b k ( x ) ∂ k , where the a

References

SHOWING 1-10 OF 19 REFERENCES

Estimates for Green's Functions of Elliptic Equations in Non-Divergence Form with Continuous Coefficients

We present a new method for the existence and pointwise estimates of a Green’s function of non-divergence form elliptic operator with Dini mean oscillation coefficients. We also present a sharp

Green's Function for Nondivergence Elliptic Operators in Two Dimensions

The Green function for second-order elliptic equations in non-divergence form is constructed when the mean oscillations of the coefficients satisfy the Dini condition and the domain has $C^{1,1}$ boundary and the Green's function is BMO in the domain and logarithmic pointwise bounds are established.

BOUNDS FOR THE FUNDAMENTAL SOLUTION OF ELLIPTIC AND PARABOLIC EQUATIONS IN NONDIVERGENCE FORM

It is shown that any elliptic or parabolic operator in nondiver- gence form with measurable coeficients has a global fundamental solution verifying certain pointwise bounds.

Alternative proof for the existence of Green's function

We present a new method for the existence of a Green's function of nod-divergence form parabolic operator with Holder continuous coefficients. We also derive a Gaussian estimate. Main ideas

Estimates for Green's matrices of elliptic systems byLp theory

SummaryWe prove existence and optimal decay properties of a Green's matrix for elliptic systems of second order. The results follow from regularity theorems in weak Lebesgue spaces which can be

Positive solutions of elliptic equations in nondivergence form and their adjoints

On considere des operateurs uniformement elliptiques de la forme L=Σ i,j=1 n a ij (X)•D XiXj 2 +Σ i=1 n b i (X)•D Xi a coefficients bornes mesurables de R n . On demontre un theoreme de comparaison

The Green function for uniformly elliptic equations

The authors discuss a generalization of the usual Green function to equations with only measurable and bounded coefficients. The existence and uniqueness as well as several other important properties

Equivalence of the Green’s functions for diffusion operators in ⁿ: a counterexample

In a smooth domain in R', the Green's functions for second-order, uniformly elliptic operators in divergence form are all proportional to the Green's function for the Laplacian [7]. In this paper we