Parabolic Harnack inequality for divergence form second order differential operators

1995 ◽  
pp. 429-467
Author(s):  
L. Saloff-Coste
Keyword(s):  
Harnack Inequality ◽  
Differential Operators ◽  
Divergence Form ◽  
Second Order ◽  
Parabolic Harnack Inequality

scholarly journals The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Alberto Cialdea ◽  
Vita Leonessa ◽  
Angelica Malaspina
Keyword(s):  
Dirichlet Problem ◽  
Differential Operators ◽  
Differential Forms ◽  
Variable Coefficients ◽  
Divergence Form ◽  
Boundary Integral ◽  
Second Order ◽  
Boundary Integral Method ◽  
Layer Potential ◽  
Partial Differential Operators

We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains ofRm(m≥3) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.

Commutators with fractional differentiation for second-order elliptic operators on ℝn

2019 ◽  
Vol 22 (02) ◽  
pp. 1950010
Author(s):  
Yanping Chen ◽  
Qingquan Deng ◽  
Yong Ding
Keyword(s):  
Differential Operators ◽  
Divergence Form ◽  
Second Order ◽  
Bounded Mean Oscillation ◽  
Fractional Differentiation ◽  
Mean Oscillation ◽  
Fractional Differential ◽  
Fractional Differential Operators ◽  
Second Order Elliptic Operators ◽  
Complex Coefficients

Let [Formula: see text] be a second-order divergence form elliptic operator and [Formula: see text] an accretive, [Formula: see text] matrix with bounded measurable complex coefficients in [Formula: see text] In this paper, we establish [Formula: see text] theory for the commutators generated by the fractional differential operators related to [Formula: see text] and bounded mean oscillation (BMO)–Sobolev functions.

DIV–CURL TYPE THEOREM, H-CONVERGENCE AND STOKES FORMULA IN THE HEISENBERG GROUP

2006 ◽  
Vol 08 (01) ◽  
pp. 67-99 ◽  
Author(s):  
BRUNO FRANCHI ◽  
NICOLETTA TCHOU ◽  
MARIA CARLA TESI
Keyword(s):  
Heisenberg Group ◽  
Vector Fields ◽  
Differential Operators ◽  
Type Theorem ◽  
Divergence Form ◽  
Second Order ◽  
Order Differential Operator ◽  
Contact Manifolds ◽  
Stokes Formula ◽  
Horizontal Vector

In this paper, we prove a div–curl type theorem in the Heisenberg group ℍ1, and then we develop a theory of H-convergence for second order differential operators in divergence form in ℍ1. The div–curl theorem requires an intrinsic notion of the curl operator in ℍ1 (that we denote by curlℍ), that turns out to be a second order differential operator in the left invariant horizontal vector fields. As an evidence of the coherence of this definition, we prove an intrinsic Stokes formula for curlℍ. Eventually, we show that this notion is related to one of the exterior differentials in Rumin's complex on contact manifolds.

scholarly journals AdS superprojectors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. I. Buchbinder ◽  
D. Hutchings ◽  
S. M. Kuzenko ◽  
M. Ponds
Keyword(s):  
Shell Model ◽  
Differential Operators ◽  
Second Order ◽  
Projection Operators ◽  
De Sitter ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

Sign in / Sign up

Export Citation Format

Share Document