Local Solvability of Quasilinear Pseudodifferential Operators of Real Principal Type
Nils Dencker
TL;DR
This paper establishes local solvability for a broad class of quasilinear pseudodifferential operators with real principal type symbols, extending previous results from second-order PDEs to more general operators using microlocal analysis.
Contribution
It generalizes the local solvability results from second-order PDEs to quasilinear pseudodifferential operators of arbitrary order with real principal type symbols.
Findings
Proves local solvability for a new class of operators.
Extends previous theorems to higher-order pseudodifferential operators.
Uses microlocalization techniques for the proof.
Abstract
In this paper we prove local solvability of quasilinear pseudodifferential operators which has homogeneous principal symbol of real principal type. This generalizes Theorem A.1 in arXiv:2403.19054, which treats the case of quasilinear partial differential operators of order 2. The proof is by microlocalization to first order model operators.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems