Estimates on the approximation of solutions to certain quasilinear elliptic equations

Autor:	Tsang-Hai Kuo
Rok vydání:	2005
Předmět:	Strong solutions Quadratic growth Nonlinear system Applied Mathematics Bounded function Convergence (routing) Mathematical analysis Structure (category theory) A priori and a posteriori Analysis Mathematics
Zdroj:	Nonlinear Analysis: Theory, Methods & Applications. 63:e427-e434
ISSN:	0362-546X
DOI:	10.1016/j.na.2005.02.018
Popis:	The convergence of approximations to solutions of nonlinear elliptic equations is closely related to the structure of the equations. As examples, we examine certain quasilinear elliptic equations with quadratic growth in the gradient defined on bounded domains. L∞ and H1 estimates on approximating solutions are performed to deduce the convergence to a solution in H01(Ω)∩L∞(Ω). In some cases, H1 a priori bound can be derived without referring to L∞ estimate. Furthermore, a W2,p(Ω) bound is also established to deduce the existence of strong solutions in W2,p(Ω)∩W01,p(Ω).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5f06b0d5ae760ef1086c0792abacb8ed https://doi.org/10.1016/j.na.2005.02.018 Zobrazit plný text záznamu Full Text from ScienceDirect