We study the Dirichlet problem for the eikonal equation: egin{displaymath} egin{cases} ha | u(x)|^2 - a(x) = 0 & extrm{in} Ocr u(x)=arphi(x) & extrm{on} partial O, end{cases} end{displaymath} without continuity assumptions on the map $a(cdot)$. We find a class of maps $a(cdot)$'s contained in the space $L^infty(O)$ for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.
Maximal generalized solution of eikonal equation / Zagatti, Sandro. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 257:1(2014), pp. 231-263. [10.1016/j.jde.2014.04.001]
Maximal generalized solution of eikonal equation
Zagatti, Sandro
2014-01-01
Abstract
We study the Dirichlet problem for the eikonal equation: egin{displaymath} egin{cases} ha | u(x)|^2 - a(x) = 0 & extrm{in} Ocr u(x)=arphi(x) & extrm{on} partial O, end{cases} end{displaymath} without continuity assumptions on the map $a(cdot)$. We find a class of maps $a(cdot)$'s contained in the space $L^infty(O)$ for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.| File | Dimensione | Formato | |
|---|---|---|---|
|
1-s2.0-S0022039614001442-main.pdf
non disponibili
Descrizione: Elsevier user license
Tipologia:
Versione Editoriale (PDF)
Licenza:
Non specificato
Dimensione
994.44 kB
Formato
Adobe PDF
|
994.44 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
