Notes on 𝑝-harmonic analysis

D'Onofrio, Luigi; Iwaniec, Tadeusz

doi:10.1090/conm/370/06828

Cited by 10 publications

(9 citation statements)

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“…In the scalar case, Equation (1.5) is just the p-Laplacian. The case of differential forms on the manifold M = R n appears in Section 6.1 of [13] where it is investigated by the method of Hodge dual systems, see also [12,Section 8].…”

Section: Relation With a Nonlinear Pdementioning

confidence: 99%

Sobolev inequalities for differential forms andL q,p -cohomology

Gol’dshtein

Troyanov

2006

J Geom Anal

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Section: Relation With a Nonlinear Pdementioning

confidence: 99%

Sobolev inequalities for differential forms andL q,p -cohomology

Gol’dshtein

Troyanov

2006

J Geom Anal

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“…The interested reader may wish to take a note of the interpolation lemmas in [1]. In the present paper I will try to elucidate some new advances of Marcinkiewicz interpolation theorem which arise from a study of the nonlinear p-harmonic type PDEs, [12,13,14,16,18,19,20]. The principal result in this paper can be described as follows:…”

Section: Arcinkiewicz Interpolation T Heorymentioning

confidence: 99%

An essay on the Interpolation Theorem of Józef Marcinkiewicz – Polish patriot

Iwaniec

2011

Banach Center Publ.

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“…For more details on p-Laplace type operators we refer to the book [15] and lecture notes [14], [30]. Applications in fluid mechanics, plastic moulding, and image processing are discussed in [4], [5], [28].…”

Section: Introductionmentioning

confidence: 99%

An Inverse Problem for the $p$-Laplacian: Boundary Determination

Salo¹,

Zhong²

2012

SIAM J. Math. Anal.

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Abstract. We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear Dirichletto-Neumann map. The result is constructive and local, and gives a method for determining the coefficient at a boundary point from measurements in a small neighborhood. The proofs work with the nonlinear equation directly instead of being based on linearization.In the complex valued case we employ complex geometrical optics type solutions based on p-harmonic exponentials, while for the real case we use p-harmonic functions first introduced by Wolff.

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Notes on 𝑝-harmonic analysis

Cited by 10 publications

References 0 publications

Sobolev inequalities for differential forms andL q,p -cohomology

Sobolev inequalities for differential forms andL q,p -cohomology

An essay on the Interpolation Theorem of Józef Marcinkiewicz – Polish patriot

An Inverse Problem for the $p$-Laplacian: Boundary Determination

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