Viscous Hamilton–Jacobi equations in exponential Orlicz hearts

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BLESSING, Jonas, Michael KUPPER, 2022. Viscous Hamilton–Jacobi equations in exponential Orlicz hearts. In: Journal de Mathématiques Pures et Appliquées. Elsevier. 163, pp. 654-672. ISSN 0021-7824. eISSN 1776-3371. Available under: doi: 10.1016/j.matpur.2022.05.018

@article{Blessing2022Visco-58053, title={Viscous Hamilton–Jacobi equations in exponential Orlicz hearts}, year={2022}, doi={10.1016/j.matpur.2022.05.018}, volume={163}, issn={0021-7824}, journal={Journal de Mathématiques Pures et Appliquées}, pages={654--672}, author={Blessing, Jonas and Kupper, Michael} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:isPartOf rdf:resource=""/> <dc:creator>Blessing, Jonas</dc:creator> <dcterms:available rdf:datatype="">2022-07-15T06:52:26Z</dcterms:available> <dc:creator>Kupper, Michael</dc:creator> <dc:contributor>Kupper, Michael</dc:contributor> <dspace:isPartOfCollection rdf:resource=""/> <dcterms:abstract xml:lang="eng">We provide a semigroup approach to viscous Hamilton–Jacobi equations. It turns out that exponential Orlicz hearts are suitable spaces to handle the (quadratic) non-linearity of the Hamiltonian. Based on an abstract extension result for nonlinear semigroups on spaces of continuous functions, we represent the solution of the viscous Hamilton–Jacobi equation as a strongly continuous convex semigroup on an exponential Orlicz heart. As a result, the solution depends continuously on the initial data. Furthermore, we determine the so-called symmetric Lipschitz set which is invariant under the semigroup. This automatically yields a priori estimates and regularity in Sobolev spaces. In particular, on the domain restricted to the symmetric Lipschitz set, the generator can be explicitly determined and linked with the viscous Hamilton–Jacobi equation.</dcterms:abstract> <dc:date rdf:datatype="">2022-07-15T06:52:26Z</dc:date> <dc:contributor>Blessing, Jonas</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:title>Viscous Hamilton–Jacobi equations in exponential Orlicz hearts</dcterms:title> <dc:language>eng</dc:language> <bibo:uri rdf:resource=""/> <dcterms:issued>2022</dcterms:issued> </rdf:Description> </rdf:RDF>

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