A Regularity Theorem for a Singular Elliptic Equation

1983 ◽  
Vol 14 (3) ◽  
pp. 223-236 ◽  
Author(s):  
P. D. Smith ◽  
Murray H. Protter
Keyword(s):  
Elliptic Equation ◽  
Regularity Theorem ◽  
Singular Elliptic Equation

Free boundary solutions to a log-singular elliptic equation

2013 ◽  
Vol 82 (1-2) ◽  
pp. 91-107 ◽  
Author(s):  
Marcelo Montenegro ◽  
Sebastián Lorca
Keyword(s):  
Elliptic Equation ◽  
Free Boundary ◽  
Singular Elliptic Equation ◽  
Boundary Solutions

scholarly journals On the Harnack inequality for degenerate and singular elliptic equations with unbounded lower order terms via sliding paraboloids

2017 ◽  
Vol 20 (01) ◽  
pp. 1750012 ◽  
Author(s):  
Nam Q. Le
Keyword(s):  
Elliptic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Elliptic Equations ◽  
Singular Elliptic Equation ◽  
Large Gradient ◽  
Singular Elliptic Equations ◽  
Monge Ampere ◽  
Lower Order Terms ◽  
Linear Degenerate

We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations. Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift.

Positive solution for a class of -singular elliptic equation

2014 ◽  
Vol 16 ◽  
pp. 163-169 ◽  
Author(s):  
Francisco Julio S.A. Corrêa ◽  
Amanda S.S. Corrêa ◽  
Giovany M. Figueiredo
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Singular Elliptic Equation

scholarly journals A uniqueness result for a singular elliptic equation with gradient term

2018 ◽  
Vol 148 (5) ◽  
pp. 983-994 ◽  
Author(s):  
José Carmona ◽  
Tommaso Leonori
Keyword(s):  
Elliptic Equation ◽  
Bounded Domain ◽  
Nonlinear Term ◽  
Uniqueness Result ◽  
Gradient Term ◽  
Singular Elliptic Equation ◽  
Uniqueness Results ◽  
Image Position ◽  
Uniqueness Of A Solution

We prove the uniqueness of a solution for a problem whose simplest model iswith k ≥ 1, 0 f ∈ L∞(Ω) and Ω is a bounded domain of ℝN, N ≥ 2. So far, uniqueness results are known for k < 1, while existence holds for any k ≥ 1 and f positive in open sets compactly embedded in a neighbourhood of the boundary. We extend the uniqueness results to the k ≥ 1 case and show, with an example, that existence does not hold if f is zero near the boundary. We even deal with the uniqueness result when f is replaced by a nonlinear term λuq with 0 < q < 1 and λ > 0.

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