On the existence of bounded generalized solutions of the Dirichlet problem for a class of nonlinear high-order elliptic equations

2015 ◽  
Vol 210 (1) ◽  
pp. 86-113 ◽  
Author(s):  
Mikhail V. Voitovich
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
High Order ◽  
Generalized Solutions ◽  
Nonlinear High Order

Solvability of Dirichlet problem for a class of degenerate nonlinear high-order equations withL1--data

2001 ◽  
Vol 47 (1) ◽  
pp. 435-446 ◽  
Author(s):  
Alexander Kovalevsky ◽  
Francesco Nicolosi
Keyword(s):  
Dirichlet Problem ◽  
High Order ◽  
Nonlinear High Order

Summability of Solutions of Dirichlet Problem for a Class of Degenerate Nonlinear High-order Equations

2003 ◽  
Vol 82 (2) ◽  
pp. 93-101 ◽  
Author(s):  
Alexander Kovalevsky ◽  
Francesco Nicolosi
Keyword(s):  
Dirichlet Problem ◽  
High Order ◽  
Nonlinear High Order

scholarly journals Measure Data Problems for a Class of Elliptic Equations with Mixed Absorption-Reaction

2021 ◽  
Vol 21 (2) ◽  
pp. 261-280
Author(s):  
Marie-Françoise Bidaut-Véron ◽  
Marta Garcia-Huidobro ◽  
Laurent Véron
Keyword(s):  
Dirichlet Problem ◽  
Compact Subset ◽  
Elliptic Equations ◽  
Radon Measure ◽  
Measure Data ◽  
Nonnegative Solutions

Abstract In the present paper, we study the existence of nonnegative solutions to the Dirichlet problem ℒ p , q M ⁢ u := - Δ ⁢ u + u p - M ⁢ | ∇ ⁡ u | q = μ {{\mathcal{L}}^{{M}}_{p,q}u:=-\Delta u+u^{p}-M|\nabla u|^{q}=\mu} in a domain Ω ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} where μ is a nonnegative Radon measure, when p > 1 {p>1} , q > 1 {q>1} and M ≥ 0 {M\geq 0} . We also give conditions under which nonnegative solutions of ℒ p , q M ⁢ u = 0 {{\mathcal{L}}^{{M}}_{p,q}u=0} in Ω ∖ K {\Omega\setminus K} , where K is a compact subset of Ω, can be extended as a solution of the same equation in Ω.

Sign in / Sign up

Export Citation Format

Share Document