Local solvability of some partial differential operators with non-smooth coefficients. (English) Zbl 1461.35105
Cicognani, Massimo (ed.) et al., Anomalies in partial differential equations. Based on talks given at the INDAM workshop, University of Rome “La Sapienza”, Rome, Italy, September 9–13, 2019. Cham: Springer. Springer INdAM Ser. 43, 277-291 (2021).
Summary: In this paper we will analyze the local solvability property of some second order linear degenerate partial differential operators with non-smooth coefficients. We will start by considering some operators with \(C^{\alpha,1}\) coefficients, with \(\alpha=0,1\), having a kind of affine structure. Next, we will study operators with a more general structure having \(C^{0,1}\) or \(L^\infty\) coefficients. In both cases the local solvability will be analyzed at multiple characteristic points where the principal symbol may possibly change sign.
For the entire collection see [Zbl 1457.35004].
For the entire collection see [Zbl 1457.35004].
MSC:
| 35G10 | Initial value problems for linear higher-order PDEs |
| 35B45 | A priori estimates in context of PDEs |
Keywords:
second order linear degenerate partial differential operators; multiple characteristic pointsReferences:
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