scholarly journals Boundary value problems for a family of domains in the Sierpinski gasket

2014 ◽  
Vol 58 (2) ◽  
pp. 497-519 ◽  
Author(s):  
Zijian Guo ◽  
Rachel Kogan ◽  
Hua Qiu ◽  
Robert S. Strichartz
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Boundary Value Problems on a Half Sierpinski Gasket

10.4171/jfg/1 ◽  
2014 ◽  
Vol 1 (1) ◽  
pp. 1-43 ◽  
Author(s):  
Weilin Li ◽  
Robert Strichartz
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

BOUNDARY VALUE PROBLEM INVOLVING THE p-LAPLACIAN ON THE SIERPIŃSKI GASKET

Fractals ◽  
2018 ◽  
Vol 26 (01) ◽  
pp. 1850007 ◽  
Author(s):  
AMIT PRIYADARSHI ◽  
ABHILASH SAHU
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

In this paper, we study the following boundary value problem involving the weak [Formula: see text]-Laplacian. [Formula: see text] [Formula: see text] where [Formula: see text] is the Sierpiński gasket in [Formula: see text], [Formula: see text] is its boundary, [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are bounded nonnegative functions. We will show the existence of at least two nontrivial weak solutions to the above problem for a certain range of [Formula: see text] using the analysis of fibering maps on suitable subsets.

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