Harmonic type approximation lemmas

By Frank Duzaar, Giuseppe Mingione. 2009

49 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/bdcbde914732536107d92355fdc22b1bdd21768d

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

The boundary regularity of non-linear parabolic systems I (2010, methodology): “For elliptic problems the technique goes back to the classical harmonic approximation lemma of De Giorgi (see [9,35]) and we refer to the recent survey paper [19] for a systematic presentation of such techniques.”
Existence of three solutions for a non-homogeneous Neumann problem through Orlicz–Sobolev spaces (2011, unknown): “The study of such problems has been stimulated by recent advances in elasticity (see [1]), fluid dynamics (see [2–4]), calculus of variations and differential equations with nonstandard growth (see [5–8]).”
Parabolic systems with polynomial growth and regularity (2011, background): “For an account of such developments we refer to the survey paper [34], where the proofs of such results can also be found together with several applications, especially in the elliptic setting.”
Sharp regularity for general Poisson equations with borderline sources (2011, background): “sult for solutions to non-homogeneous Poisson Equations (1.5) that will play a fundamental role in the proof of Theorem 3.1 and Theorem 4.1. In fact Lemma 2.1 follows as a consequence of Lemma 3.2 in [8]. We include here a proof for completeness purposes. 4 Lemma 2.1. Let u ∈ W1,p(B 1) be a weak sol”
Regularity for general functionals with double phase (2017, methodology): “Beside the above quantitative harmonic approximation, we report the following more standard version, which is close to the ones described in [23, 24].”