The p-harmonic approximation and the regularity of p-harmonic maps

By Frank Duzaar, Giuseppe Mingione. 2004

133 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4e9492774bebf898455de5740232abc4e98ed2a2

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Everywhere regularity of functionals with φ-growth (2009, background): “The following result generalizes Lemma 3 of [ 9 ] to the context of convex functions.”
Harmonic type approximation lemmas (2009, background): “While some partial results in this direction have been obtained in [47,39], the full statement has been finally achieved in [28], and naturally reads as Lemma 3.”
Gradient estimates via linear and nonlinear potentials (2010, background): “This result is standard in the case of the p-Laplacian equation – see for instance [7] and references therein – and it is more in general known to hold for minima of certain functionals of the Calculus of Variations with p-growth; moreover, it extends to minimizers of the p-Dirichlet functional (4.”
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications (2008, methodology): “To name a few, we refer to the articles with applications in the calculus of variations [1,19,20,27,35,36], in the existence theory of partial diﬀerential equations [13,18,23,34,37] and in the regularity theory [2,14].”
Second order parabolic systems, optimal regularity, and singular sets of solutions (2005, background): “Later this has been generalized to the degenerate elliptic prob the authors [12,13].”
Sobolev Mappings between Manifolds and Metric Spaces (2009, unknown): “[4], [ 16 ], [34], [41], [42], [48], [65], [69], [79], [80], [83], [84].”
Parabolic systems with polynomial growth and regularity (2011, methodology): “We like to remark that here, differently from the elliptic case [44, 31], the results are obtained with Harmonic Analysis-free proofs, since classical tools as singular integrals and maximal operators cannot be used for evolutionary problems with polynomial growth.”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, methodology): “The proof of Theorem 4.13 offers an example of application of the " p-harmonic approximation lemma " , obtained in [100], that extends the original De Giorgi's one [78] [283] to the case p = 2.”
The boundary regularity of non-linear parabolic systems I (2010, background): “the case p = 2, and later extended to the case of systems with polynomial growth p 2 [20,19,18,17].”