Carleman type inequalities for fractional relativistic operators

TL;DR

This paper develops Carleman estimates for fractional relativistic operators, using spectral methods to analyze solutions to related heat equations, and establishes monotonicity and convexity properties of energy functionals.

Contribution

It introduces novel Carleman estimates for fractional relativistic operators employing spectral techniques and explores properties of solutions to associated heat equations.

Findings

Derived Carleman estimates with linear exponential weights.

Proved monotonicity inequalities for energy functionals.

Established convexity properties of certain energy functionals.

Abstract

In this paper we derive Carleman estimates for the fractional relativistic operator. We consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity of certain energy functionals to deduce Carleman estimates with linear exponential weight. Our approach is based on spectral methods and functional calculus.