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A local energy
estimate for 2-dimensional Dirichlet wave equations
Kellan Hepditch and Jason Metcalfe |
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Vol. 16 (2023), No. 3, 483–492
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Abstract |
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We examine a variant of the integrated local energy estimate for -dimensional Dirichlet wave equations exterior to star-shaped obstacles. The classical bound on the solution, rather than the derivative, is not typically available in two spatial dimensions. Using an argument inspired by the -weighted method of Dafermos and Rodnianski and taking advantage of the Dirichlet boundary conditions allow for the recovery of such a term when the initial energy is appropriately weighted. |
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Keywords
wave equation, local energy estimate, exterior domain
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Mathematical Subject Classification
Primary: 35L71, 35L05
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Milestones
Received: 7 February 2022
Revised: 15 June 2022
Accepted: 11 September 2022
Published: 10 August 2023
Communicated by Suzanne Lenhart
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Authors |
| Kellan Hepditch | |
| Cedar Ridge High School Hillsborough, NC United States |
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| Jason Metcalfe | |
| Department of Mathematics University of North Carolina Chapel Hill, NC United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
