scholarly journals A Boundary Harnack Principle for Infinity-Laplacian and Some Related Results

2007 ◽  
Vol 2007 ◽  
pp. 1-17 ◽  
Author(s):  
Tilak Bhattacharya
Keyword(s):  
Boundary Harnack Principle ◽  
Infinity Laplacian

scholarly journals Boundary Harnack principle for subordinate Brownian motions

2009 ◽  
Vol 119 (5) ◽  
pp. 1601-1631 ◽  
Author(s):  
Panki Kim ◽  
Renming Song ◽  
Zoran Vondraček
Keyword(s):  
Boundary Harnack Principle ◽  
Brownian Motions

scholarly journals Radial symmetry for an elliptic PDE with a free boundary

2021 ◽  
Vol 8 (26) ◽  
pp. 311-319
Author(s):  
Layan El Hajj ◽  
Henrik Shahgholian
Keyword(s):  
Free Boundary ◽  
Radial Symmetry ◽  
Regularity Of Solutions ◽  
Elliptic Pde ◽  
Linear Elliptic Equation ◽  
Boundary Harnack Principle ◽  
Partial Differential ◽  
Content Type ◽  
Moving Plane ◽  
Plane Technique

In this paper we prove symmetry for solutions to the semi-linear elliptic equation Δ u = f ( u )  in  B 1 , 0 ≤ u > M ,  in  B 1 , u = M ,  on  ∂ B 1 , \begin{equation*} \Delta u = f(u) \quad \text { in } B_1, \qquad 0 \leq u > M, \quad \text { in } B_1, \qquad u = M, \quad \text { on } \partial B_1, \end{equation*} where M > 0 M>0 is a constant, and B 1 B_1 is the unit ball. Under certain assumptions on the r.h.s. f ( u ) f (u) , the C 1 C^1 -regularity of the free boundary ∂ { u > 0 } \partial \{u>0\} and a second order asymptotic expansion for u u at free boundary points, we derive the spherical symmetry of solutions. A key tool, in addition to the classical moving plane technique, is a boundary Harnack principle (with r.h.s.) that replaces Serrin’s celebrated boundary point lemma, which is not available in our case due to lack of C 2 C^2 -regularity of solutions.

Large solutions for the infinity Laplacian

2008 ◽  
Vol 1 (3) ◽  
Author(s):  
Petri Juutinen ◽  
Julio D. Rossi
Keyword(s):  
Infinity Laplacian ◽  
Large Solutions

scholarly journals The tug-of-war without noise and the infinity Laplacian in a wedge

2013 ◽  
Vol 123 (12) ◽  
pp. 4219-4255
Author(s):  
Dante DeBlassie ◽  
Robert G. Smits
Keyword(s):  
Infinity Laplacian

scholarly journals A Symmetry Problem for the Infinity Laplacian: Fig. 1.

2014 ◽  
Vol 2015 (18) ◽  
pp. 8411-8436 ◽  
Author(s):  
Graziano Crasta ◽  
Ilaria Fragalà
Keyword(s):  
Infinity Laplacian ◽  
Symmetry Problem

A weighted eigenvalue problem of the biased infinity Laplacian *

Nonlinearity ◽  
2021 ◽  
Vol 34 (2) ◽  
pp. 1197-1237
Author(s):  
Fang Liu ◽  
Xiao-Ping Yang
Keyword(s):  
Eigenvalue Problem ◽  
Infinity Laplacian
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