Complex and real valued solutions for fractoinal Helmholtz equation
Zifei Shen, Shuijin Zhang
TL;DR
This paper investigates the fractional Helmholtz equation, establishing boundedness estimates for the resolvent and developing a dual variational framework to find complex and real solutions, advancing understanding of fractional PDEs.
Contribution
It introduces a new approach to analyze the fractional Helmholtz equation by establishing resolvent estimates and a variational method for real solutions.
Findings
Established boundedness estimates for the fractional Helmholtz resolvent.
Derived nontrivial complex valued solutions in Lq(Rn).
Obtained real valued solutions via a dual variational framework.
Abstract
In this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation, By establishing the boundedness estimate for the resolvent of fractional Helmholtz operator, we obtain the nontrivial Lq(Rn) complex valued solutions for (0.1). By setting up a dual variational framework, we also obtain the real valued solutions for (0.1) via a non-vanishing principle.
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Taxonomy
TopicsNumerical methods in engineering · Numerical methods in inverse problems · Advanced Mathematical Modeling in Engineering