scholarly journals Boundary regularity of weak solutions to nonlinear elliptic obstacle problems

2006 ◽  
Vol 2006 ◽  
pp. 1-15
Author(s):  
M. Junxia ◽  
Chu Yuming
Keyword(s):  
Weak Solutions ◽  
Boundary Regularity ◽  
Obstacle Problems ◽  
Nonlinear Elliptic ◽  
Regularity Of Weak Solutions

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.

scholarly journals Regularity of Weak Solutions to Elliptic Problem with Irregular Data

2022 ◽  
Author(s):  
Abdelaziz Hellal
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Growth Conditions ◽  
Variable Exponents ◽  
Bounded Subset ◽  
Lebesgue Spaces ◽  
Nonlinear Elliptic ◽  
Regularity Of Weak Solutions ◽  
Irregular Data

This paper is concerned with the study of the nonlinear elliptic equations in a bounded subset Ω ⊂ RN Au = f, where A is an operator of Leray-Lions type acted from the space W1,p(·)0(Ω) into its dual. when the second term f belongs to Lm(·), with m(·) > 1 being small. we prove existence and regularity of weak solutions for this class of problems p(x)-growth conditions. The functional framework involves Sobolev spaces with variable exponents as well as Lebesgue spaces with variable exponents.

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