Global second order Sobolev-regularity of p-harmonic functions

On the second-order regularity of solutions to the parabolic p-Laplace equation

“…For the statement of the lemma, we introduce notation that is similar to [28]. This notation serves only for the lemma and its application Section 4.3.…”

“…We show that if the growth rates of ϕ and ψ are close enough in a suitable quantitative sense, then it is possible to derive a Caccioppoli-type inequality for V ψ (∇u). The proof relies on Cordes matrix inequalities [16] (see also [43]) and a pointwise inequality from [28].…”

“…Let us elaborate on the essence of our proofs. The main technical tool is a pointwise estimate, Lemma 2.1, which can be found in [28,Lemma 3.2,Corollary 3.3]. It is based on Cordes' matrix inequalities [16], see also [43].…”