scholarly journals On the boundary regularity of weak solutions to the MHD system

2011 ◽  
Vol 178 (3) ◽  
pp. 243-264 ◽  
Author(s):  
V. Vyalov ◽  
T. Shilkin
Keyword(s):  
Weak Solutions ◽  
Boundary Regularity ◽  
Regularity Of Weak Solutions ◽  
Mhd System

scholarly journals Interior and boundary regularity results for strongly nonhomogeneous p,q-fractional problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jacques Giacomoni ◽  
Deepak Kumar ◽  
Konijeti Sreenadh
Keyword(s):  
Maximum Principle ◽  
Comparison Principle ◽  
Weak Solutions ◽  
Global Regularity ◽  
Boundary Regularity ◽  
Holder Continuity ◽  
Regularity Of Weak Solutions ◽  
Regularity Results ◽  
Boundary Estimates ◽  
Strong Comparison Principle

Abstract In this article, we deal with the global regularity of weak solutions to a class of problems involving the fractional ( p , q ) {(p,q)} -Laplacian, denoted by ( - Δ ) p s 1 + ( - Δ ) q s 2 {(-\Delta)^{s_{1}}_{p}+(-\Delta)^{s_{2}}_{q}} for s 2 , s 1 ∈ ( 0 , 1 ) {s_{2},s_{1}\in(0,1)} and 1 < p , q < ∞ {1<p,q<\infty} . We establish completely new Hölder continuity results, up to the boundary, for the weak solutions to fractional ( p , q ) {(p,q)} -problems involving singular as well as regular nonlinearities. Moreover, as applications to boundary estimates, we establish a new Hopf-type maximum principle and a strong comparison principle in both situations.

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