A note on estimates for elliptic systems with L1 data

Raiță, Bogdan; Spector, Daniel

doi:10.1016/j.crma.2019.11.007

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Cited by 2 publications

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References 12 publications

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“…We recall that the cocanceling assumption is very mild: As was observed in [10,15,28], failure of this assumption is equivalent to the existence of an unconstrained subspace of L(D)-free fields.…”

Section: Introductionmentioning

confidence: 92%

Endpoint $L^1$ estimates for Hodge systems

Hernandez,

Raita,

Spector

2021

Preprint

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Section: Introductionmentioning

confidence: 92%

Endpoint $L^1$ estimates for Hodge systems

Hernandez,

Raita,

Spector

2021

Preprint

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“…We recall that the cocanceling assumption is very mild: As was observed in [9,18,32], failure of this assumption is equivalent to the existence of an unconstrained subspace of L(D)-free fields.…”

Section: Introductionmentioning

confidence: 93%

Endpoint $$L^1$$ estimates for Hodge systems

2022

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Let $$d\ge 2$$ d ≥ 2 . In this paper we give a simple proof of the endpoint Besov-Lorentz estimate $$\begin{aligned} \Vert I_\alpha F\Vert _{{\dot{B}}^{0,1}_{d/(d-\alpha ),1}(\mathbb {R}^d;\mathbb {R}^k)} \le C \Vert F \Vert _{L^1(\mathbb {R}^d;\mathbb {R}^k)} \end{aligned}$$ ‖ I α F ‖ B ˙ d / ( d - α ) , 1 0 , 1 ( R d ; R k ) ≤ C ‖ F ‖ L 1 ( R d ; R k ) for all $$F \in L^1(\mathbb {R}^d;\mathbb {R}^k)$$ F ∈ L 1 ( R d ; R k ) which satisfy a first order cocancelling differential constraint, where $$\alpha \in (0,d)$$ α ∈ ( 0 , d ) and $$I_\alpha $$ I α is a Riesz potential. We show how this implies endpoint Besov–Lorentz estimates for Hodge systems with $$L^1$$ L 1 data via fractional integration for exterior derivatives.

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A note on estimates for elliptic systems with L1 data

Abstract: In this paper we give necessary and sufficient conditions on the compatibility of a kth order homogeneous linear elliptic differential operator A and differential constraint C for solutions of Au = f subject to Cf = 0 in R n to satisfy the estimates

Cited by 2 publications

References 12 publications

Endpoint $L^1$ estimates for Hodge systems

Endpoint $L^1$ estimates for Hodge systems

Endpoint $$L^1$$ estimates for Hodge systems

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