higher integrability
Recently Published Documents


TOTAL DOCUMENTS

117
(FIVE YEARS 33)

H-INDEX

14
(FIVE YEARS 3)

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3015
Author(s):  
Gregory A. Chechkin

In this paper, we consider an elliptic problem in a domain perforated along the boundary. By setting a homogeneous Dirichlet condition on the boundary of the cavities and a homogeneous Neumann condition on the outer boundary of the domain, we prove higher integrability of the gradient of the solution to the problem.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arturo Popoli

Abstract We study the higher integrability of weights satisfying a reverse Hölder inequality ( ⨏ I u β ) 1 β ≤ B ⁢ ( ⨏ I u α ) 1 α {\biggl{(}\fint_{I}u^{\beta}\biggr{)}^{\frac{1}{\beta}}}\leq B{\biggl{(}\fint_{I}u^{\alpha}\biggr{)}^{\frac{1}{\alpha}}} for some B > 1 B>1 and given α < β \alpha<\beta , in the limit cases when α ∈ { - ∞ , 0 } \alpha\in\{-\infty,0\} and/or β ∈ { 0 , + ∞ } \beta\in\{0,+\infty\} . The results apply to the Gehring and Muckenhoupt weights and their corresponding limit classes.


Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca

AbstractWe consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The associated obstacle problem is also solved. Finally, we show higher integrability of a solution to the Dirichlet problem when the datum is more regular.


Author(s):  
Lukas Koch

AbstractWe prove global $$W^{1,q}({\varOmega },{\mathbb {R}}^m)$$ W 1 , q ( Ω , R m ) -regularity for minimisers of convex functionals of the form $${\mathscr {F}}(u)=\int _{\varOmega } F(x,Du)\,{\mathrm{d}}x$$ F ( u ) = ∫ Ω F ( x , D u ) d x .$$W^{1,q}({\varOmega },{\mathbb {R}}^m)$$ W 1 , q ( Ω , R m ) regularity is also proven for minimisers of the associated relaxed functional. Our main assumptions on F(x, z) are a uniform $$\alpha $$ α -Hölder continuity assumption in x and controlled (p, q)-growth conditions in z with $$q<\frac{(n+\alpha )p}{n}$$ q < ( n + α ) p n .


Author(s):  
Mathias Schäffner

AbstractWe consider autonomous integral functionals of the form $$\begin{aligned} {\mathcal {F}}[u]:=\int _\varOmega f(D u)\,dx \quad \text{ where } u:\varOmega \rightarrow {\mathbb {R}}^N, N\ge 1, \end{aligned}$$ F [ u ] : = ∫ Ω f ( D u ) d x where u : Ω → R N , N ≥ 1 , where the convex integrand f satisfies controlled (p, q)-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of $${\mathcal {F}}$$ F assuming $$\frac{q}{p}<1+\frac{2}{n-1}$$ q p < 1 + 2 n - 1 , $$n\ge 3$$ n ≥ 3 . This improves earlier results valid under the more restrictive assumption $$\frac{q}{p}<1+\frac{2}{n}$$ q p < 1 + 2 n .


Author(s):  
Jan Burczak ◽  
Wojciech S. Ożański ◽  
Gregory Seregin

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local smoothness of solutions.


Sign in / Sign up

Export Citation Format

Share Document