The article investigates Gevrey regularity and summability in formal solutions of inhomogeneous linear PDE systems with analytic coefficients, highlighting their implications.
Key Points
This paper aims to explore the Gevrey regularity and summability of solutions to inhomogeneous linear systems of PDEs.
Investigated formal solutions of inhomogeneous linear PDE systems with analytic coefficients.
Analyzed the dichotomy of Gevrey regularity based on the s-Gevrey regularity of the inhomogeneity.
Established necessary and sufficient conditions for 1/s0-summability in specific directions.
For s ≥ s0, solutions inherit the Gevrey regularity of the inhomogeneity.
For s < s0, solutions maintain the s0-Gevrey regularity dictated by the initial system's structure.
Provided examples that illustrate the derived results.