@article{3c94cc54955244d5beecb3bbd43c617a,
title = "On an elastic model arising from volcanology: An analysis of the direct and inverse problem",
abstract = "In this paper we investigate a mathematical model arising from volcanology describing surface deformation effects generated by a magma chamber embedded into Earth's interior and exerting on it a uniform hydrostatic pressure. The modeling assumptions translate mathematically into a Neumann boundary value problem for the classical Lam{\'e} system in a half-space with an embedded pressurized cavity. We establish well-posedness of the problem in suitable weighted Sobolev spaces and analyse the inverse problem of determining the pressurized cavity from partial measurements of the displacement field proving uniqueness and stability estimates.",
keywords = "Half-space, Inverse problem, Lam{\'e} system, Neumann problem, Stability estimates, Weighted Sobolev spaces",
author = "A. Aspri and E. Beretta and E. Rosset",
note = "Funding Information: The authors thank Prof. Cherif Amrouche for his kindness in suggesting and providing some useful papers and for his enlightening advice. Andrea Aspri and Elena Beretta thank the New York University in Abu Dhabi (EAU) for its kind hospitality that permitted a further development of the present research. Andrea Aspri thanks {\"O}AW (Austrian Academy of Sciences) and RICAM for giving him the possibility to finish this paper. Edi Rosset is supported by FRA2016 “Problemi inversi, dalla stabilit{\`a} alla ricostruzione”, Universit{\`a} degli Studi di Trieste and by Progetto GNAMPA 2017 “Analisi di problemi inversi: stabilit{\`a} e ricostruzione”, Istituto Nazionale di Alta Matematica ( INdAM ). Funding Information: The authors thank Prof. Cherif Amrouche for his kindness in suggesting and providing some useful papers and for his enlightening advice. Andrea Aspri and Elena Beretta thank the New York University in Abu Dhabi (EAU) for its kind hospitality that permitted a further development of the present research. Andrea Aspri thanks ?AW (Austrian Academy of Sciences) and RICAM for giving him the possibility to finish this paper. Edi Rosset is supported by FRA2016 ?Problemi inversi, dalla stabilit? alla ricostruzione?, Universit? degli Studi di Trieste and by Progetto GNAMPA 2017 ?Analisi di problemi inversi: stabilit? e ricostruzione?, Istituto Nazionale di Alta Matematica (INdAM). Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",
year = "2018",
month = dec,
day = "15",
doi = "10.1016/j.jde.2018.07.031",
language = "English (US)",
volume = "265",
pages = "6400--6423",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "12",
}