Partial Regularity for Minimizers of Free Discontinuity Problems with p-th Growth

2000 ◽  
pp. 153-169
Author(s):  
A. Leaci
Keyword(s):  
Partial Regularity ◽  
Free Discontinuity Problems

scholarly journals Partial regularity of stable solutions to the fractional Geľfand-Liouville equation

2021 ◽  
Vol 10 (1) ◽  
pp. 1316-1327
Author(s):  
Ali Hyder ◽  
Wen Yang
Keyword(s):  
Liouville Equation ◽  
Weak Solutions ◽  
Partial Regularity ◽  
Singular Set ◽  
Stable Solutions ◽  
Gelfand Problem

Abstract We analyze stable weak solutions to the fractional Geľfand problem ( − Δ ) s u = e u i n Ω ⊂ R n . $$\begin{array}{} \displaystyle (-{\it\Delta})^su = e^u\quad\mathrm{in}\quad {\it\Omega}\subset\mathbb{R}^n. \end{array}$$ We prove that the dimension of the singular set is at most n − 10s.

scholarly journals Partial regularity and amplitude

2006 ◽  
Vol 128 (4) ◽  
pp. 1025-1056 ◽  
Author(s):  
Donu Arapura
Keyword(s):  
Partial Regularity
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