We study the Sobolev regularity of \(p\)-harmonic functions. We show that \(|Du|^{\frac{p-2+s}{2}}Du\) belongs to the Sobolev space \(W^{1,2}_{\operatorname{loc}}\), \(s>-1-\frac{p-1}{n-1}\), for any \(p\)-harmonic function \(u\). The proof is based on an elementary inequality
Abstract. We show that if u 2 C1(Ω) satises the p-Laplace equation div(jrujp−2ru) = 0 in Ω n fx: u(...
In this thesis we first implement iteration methods for fractional difference quotients of weak solu...
Two scales of harmonic Hardy-Sobolev spaces are introduced and their boundary regularity is studied....
We prove a global version of the classical result that $p$-harmonic functions belong to $W^{2,2}_{lo...
In this thesis we are concerned with estimating the regularity of ${\cal A}$-harmonic differential f...
We prove a global version of the classical result that p-harmonic functions belong to W-loc(2,2) for...
Abstract. Using the theory of Sobolev spaces on a metric measure space we are able to apply calculus...
In this paper we prove that any very weak $s$-harmonic function $u$ in the unit ball $B$ is locally ...
Abstract. The paper is concerned with the A-harmonic equation div[〈G(x)∇u,∇u〉(p−2)/2G(x)∇u] = 0 whe...
Abstract. Via a random construction we establish necessary conditions for Lp(`q) in-equalities for c...
Abstract. In this paper, the following result is given by using Hodge decomposition and weak reverse...
We extend to the degenerate case p = 2, Simon’s approach to the classical regularity theory of harmo...
We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Eucli...
We consider weak solutions to a class of Dirichlet boundary value problems involving the p-Laplace o...
Abstract. We apply subelliptic Cordes conditions and Talenti-Pucci type inequalities to prove W 2,2 ...
Abstract. We show that if u 2 C1(Ω) satises the p-Laplace equation div(jrujp−2ru) = 0 in Ω n fx: u(...
In this thesis we first implement iteration methods for fractional difference quotients of weak solu...
Two scales of harmonic Hardy-Sobolev spaces are introduced and their boundary regularity is studied....
We prove a global version of the classical result that $p$-harmonic functions belong to $W^{2,2}_{lo...
In this thesis we are concerned with estimating the regularity of ${\cal A}$-harmonic differential f...
We prove a global version of the classical result that p-harmonic functions belong to W-loc(2,2) for...
Abstract. Using the theory of Sobolev spaces on a metric measure space we are able to apply calculus...
In this paper we prove that any very weak $s$-harmonic function $u$ in the unit ball $B$ is locally ...
Abstract. The paper is concerned with the A-harmonic equation div[〈G(x)∇u,∇u〉(p−2)/2G(x)∇u] = 0 whe...
Abstract. Via a random construction we establish necessary conditions for Lp(`q) in-equalities for c...
Abstract. In this paper, the following result is given by using Hodge decomposition and weak reverse...
We extend to the degenerate case p = 2, Simon’s approach to the classical regularity theory of harmo...
We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Eucli...
We consider weak solutions to a class of Dirichlet boundary value problems involving the p-Laplace o...
Abstract. We apply subelliptic Cordes conditions and Talenti-Pucci type inequalities to prove W 2,2 ...
Abstract. We show that if u 2 C1(Ω) satises the p-Laplace equation div(jrujp−2ru) = 0 in Ω n fx: u(...
In this thesis we first implement iteration methods for fractional difference quotients of weak solu...
Two scales of harmonic Hardy-Sobolev spaces are introduced and their boundary regularity is studied....
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