Gradient Estimates for Elliptic Operators with Second-Order Discontinuous Coefficients

2019 ◽  
Vol 16 (6) ◽  
Author(s):  
G. Metafune ◽  
L. Negro ◽  
C. Spina
Keyword(s):  
Discontinuous Coefficients ◽  
Elliptic Operators ◽  
Second Order ◽  
Gradient Estimates

scholarly journals Maximal regularity for elliptic operators with second-order discontinuous coefficients

2020 ◽  
Author(s):  
G. Metafune ◽  
L. Negro ◽  
C. Spina
Keyword(s):  
Elliptic Operator ◽  
Maximal Regularity ◽  
Discontinuous Coefficients ◽  
Elliptic Operators ◽  
Second Order ◽  
Parabolic Problems ◽  
Order Elliptic Operator

Abstract We prove maximal regularity for parabolic problems associated to the second-order elliptic operator $$\begin{aligned} L =\Delta +(a-1)\sum _{i,j=1}^N\frac{x_ix_j}{|x|^2}D_{ij}+c\frac{x}{|x|^2}\cdot \nabla -b|x|^{-2} \end{aligned}$$ L = Δ + ( a - 1 ) ∑ i , j = 1 N x i x j | x | 2 D ij + c x | x | 2 · ∇ - b | x | - 2 with $$a>0$$ a > 0 and $$b,\ c$$ b , c real coefficients.

Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients

2020 ◽  
Vol 32 (2) ◽  
pp. 399-415 ◽  
Author(s):  
Luigi Negro ◽  
Chiara Spina
Keyword(s):  
Asymptotic Behaviour ◽  
Elliptic Operator ◽  
Discontinuous Coefficients ◽  
Elliptic Operators ◽  
Second Order ◽  
Parabolic Problems ◽  
Order Elliptic Operator

AbstractWe study the behaviour at infinity, in suitable weighted {L^{p}}-norms, of solutions of parabolic problems associated to the second order elliptic operatorL=\Delta+(a-1)\sum_{i,j=1}^{N}\frac{x_{i}x_{j}}{|x|^{2}}D_{ij}+c\frac{x}{|x|^{% 2}}\cdot\nabla-b|x|^{-2},where {a>0} and {b,c\in\mathbb{R}}.

scholarly journals Heat Kernels of Second Order Complex Elliptic Operators and Applications

1998 ◽  
Vol 152 (1) ◽  
pp. 22-73 ◽  
Author(s):  
Pascal Auscher ◽  
Alan McIntosh ◽  
Philippe Tchamitchian
Keyword(s):  
Elliptic Operators ◽  
Heat Kernels ◽  
Second Order ◽  
Order Complex
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