Systems of fully nonlinear degenerate elliptic obstacle problems with Dirichlet boundary conditions
dc.contributor.author | Andronicou, Savvas | en |
dc.contributor.author | Milakis, Emmanouil | en |
dc.creator | Andronicou, Savvas | en |
dc.creator | Milakis, Emmanouil | en |
dc.date.accessioned | 2023-12-17T11:16:05Z | |
dc.date.available | 2023-12-17T11:16:05Z | |
dc.date.issued | 2023 | |
dc.identifier.uri | http://gnosis.library.ucy.ac.cy/handle/7/65810 | en |
dc.description.abstract | In this paper, we prove existence and uniqueness of viscosity solutions to the following system: For i ∈ {1, 2,..., m} min F y, x, ui(y, x), Dui(y, x), D2ui(y, x) , ui(y, x) − max j=i u j(y, x) − ci j(y, x) = 0,(y, x) ∈ L ui(0, x) = gi(x), x ∈ , ¯ ui(y, x) = fi(y, x), (y, x) ∈ (0, L) × ∂ where ⊂ Rn is a bounded domain, L := (0, L)× and F : [0, L]×Rn×R×Rn×Sn → R is a general second-order partial differential operator which covers even the fully nonlinear case. (We will call a second-order partial differential operator F : [0, L] × Rn × R × Rn × Sn → R fully nonlinear if and only if, it has the following form F y, x, u, Dxu, D2 x xu := |α|=2 αα y, x, u, Dxu, D2 x xu Dαu(y, x) + α0 (y, x, u, Dxu) with the restriction that at least one of the functional coefficients αα, |α| = 2, contains a partial derivative term of second order.) Moreover, F belongs to an appropriate subclass of degenerate elliptic operators. Regarding uniqueness, we establish a comparison principle for viscosity sub and supersolutions of the Dirichlet problem. This system appears among others in the theory of the so-called optimal switching problems on bounded domains. | en |
dc.language.iso | eng | en |
dc.publisher | Springer | en |
dc.source | Annali di Matematica Pura ed Applicata | it |
dc.source.uri | https://link.springer.com/article/10.1007/s10231-023-01343-w#citeas | en |
dc.subject | Optimal switching problems | en |
dc.subject | Fully nonlinear equations | en |
dc.subject | Viscosity solutions | en |
dc.title | Systems of fully nonlinear degenerate elliptic obstacle problems with Dirichlet boundary conditions | en |
dc.type | info:eu-repo/semantics/article | en |
dc.identifier.doi | https://doi.org/10.1007/s10231-023-01343-w | en |
dc.description.volume | 202 | en |
dc.description.startingpage | 2861 | en |
dc.description.endingpage | 2901 | en |
dc.author.faculty | Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences | |
dc.author.department | Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics | |
dc.type.uhtype | Article | en |
dc.contributor.orcid | Milakis, Emmanouil [0000-0001-8538-1129] | |
dc.type.subtype | SCIENTIFIC_JOURNAL | en |
dc.gnosis.orcid | 0000-0001-8538-1129 |
Files in this item
Files | Size | Format | View |
---|---|---|---|
There are no files associated with this item. |