The Green function estimates for strongly elliptic systems of second order. (English) Zbl 1130.35042
This paper deals with the study of Green’s functions associated to second order strongly elliptic systems of divergence type in a domain \(\Omega\subset\mathbb R^n\), with \(n\geq 3\). The main result establishes that if an elliptic system has the property that all weak solutions of the system are locally Hölder continuous, then it has the Green’s matrix in \(\Omega\). The standard properties of Green’s matrix including pointwise bounds, \(L^p\) and weak \(L^p\) estimates for its derivatives are also studied for such elliptic systems.
Reviewer: Teodora-Liliana Rădulescu (Craiova)
MathOverflow Questions:
References for Green functions of \(\nabla \cdot a \nabla\) on a domain with \(a \in L^\infty\)MSC:
| 35J45 | Systems of elliptic equations, general (MSC2000) |
| 35A08 | Fundamental solutions to PDEs |
| 35B45 | A priori estimates in context of PDEs |
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