The $L^{p}-L^{\acute{p}}$ Estimate for the Schr\"{o}dinger Equation on the Half-Line

TL;DR

This paper establishes $L^{p}-L^{ ilde{p}}$ estimates for the Schrödinger equation on the half-line with Dirichlet boundary conditions, advancing understanding of boundary effects in dispersive PDEs.

Contribution

It provides the first proof of $L^{p}-L^{ ilde{p}}$ estimates for the Schrödinger equation on the half-line with boundary conditions, extending dispersive analysis.

Findings

Proves $L^{p}-L^{ ilde{p}}$ estimates for the half-line Schrödinger equation.

Handles homogeneous Dirichlet boundary conditions.

Enhances boundary value problem analysis for dispersive PDEs.

Abstract

In this paper we prove the $L^{p}-L^{\acute{p}}$ estimate for the Schr\"{o}dinger equation on the half-line and with homogeneous Dirichlet boundary condition at the origin.