L^p-quasicontractiveness and Kernel estimates for semigroups generated by systems of elliptic operators

2025/10/08 by Angiuli, L., Mangino, E. M., Lorenzi, L.
#Analysis of PDEs (math.AP) #FOS: Mathematics #Systems of elliptic operators #consistent strongly continuous analytic semigroups #generation results #kernel estimates #unbounded coefficients

paper · doi:10.48550/arxiv.2510.07216

Abstract

This paper focuses on systems of strongly coupled elliptic operators whose coefficients may be unbounded and are defined on a domain Ω⊆ ℝ^d. It is shown that a quasi-contractive semigroup in L^p-spaces can be associated with such operators for values of p belonging to an interval that contains 2 as an interior point. Then, under refined assumptions and considering systems of elliptic operators coupled up to first order, new kernel estimates are established with respect to a distance function that accounts for the growth of the diffusion coefficients and the potential term at infinity.

Citations

• Bounded H^∞-calculus for vectorial-valued operators with Gaussian kernel estimates
• Kernel estimates for parabolic systems of partial differential equations with unbounded coefficients
• L^p Maximal regularity for vector-valued Schrödinger operators
• Strongly coupled Schroedinger operators in L^p(R^d;C^m)
• Generation results for vector-valued elliptic operators with unbounded coefficients in L^p spaces
• Vector-valued Schrödinger operators on L^p-spaces
• Convexity of power functions and bilinear embedding for divergence-form\n operators with complex coefficients
• L^p-estimates for parabolic systems with unbounded coefficients coupled at zero and first order
• Criterion for the L^p-dissipativity of second order differential operators with complex coefficients

Related

• Explicit improvements for L^p-estimates related to elliptic systems
• Generation of semigroups associated to strongly coupled elliptic operator in L^p(\mathbb R^d;\mathbb R^m)
• Elliptic operators with unbounded diffusion coefficients in Lp spaces
• Generation results for vector-valued elliptic operators with unbounded coefficients in L^p spaces
• Strongly coupled Schroedinger operators in L^p(R^d;C^m)