# The restriction theorem for fully nonlinear subequations

F. Reese Harvey^{[1]}; H. Blaine Lawson^{[2]}

- [1] Rice University Department of Mathematics P.O. Box 1892 MS-172 Houston, 77251(Texas)
- [2] Stony Brook University Department of Mathematics Stony Brook NY, 11794-3651 (USA)

Annales de l’institut Fourier (2014)

- Volume: 64, Issue: 1, page 217-265
- ISSN: 0373-0956

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topHarvey, F. Reese, and Lawson, H. Blaine. "The restriction theorem for fully nonlinear subequations." Annales de l’institut Fourier 64.1 (2014): 217-265. <http://eudml.org/doc/275604>.

@article{Harvey2014,

abstract = {Let $X$ be a submanifold of a manifold $Z$. We address the question: When do viscosity subsolutions of a fully nonlinear PDE on $Z$, restrict to be viscosity subsolutions of the restricted subequation on $X$? This is not always true, and conditions are required. We first prove a basic result which, in theory, can be applied to any subequation. Then two definitive results are obtained. The first applies to any “geometrically defined” subequation, and the second to any subequation which can be transformed to a constant coefficient (i.e., euclidean) model. This provides a long list of geometrically and analytically interesting cases where restriction holds.},

affiliation = {Rice University Department of Mathematics P.O. Box 1892 MS-172 Houston, 77251(Texas); Stony Brook University Department of Mathematics Stony Brook NY, 11794-3651 (USA)},

author = {Harvey, F. Reese, Lawson, H. Blaine},

journal = {Annales de l’institut Fourier},

keywords = {Viscosity solution; viscosity subsolution; nonlinear second-order elliptic equations; restriction; submanifold; pluripotential theory; viscosity solution},

language = {eng},

number = {1},

pages = {217-265},

publisher = {Association des Annales de l’institut Fourier},

title = {The restriction theorem for fully nonlinear subequations},

url = {http://eudml.org/doc/275604},

volume = {64},

year = {2014},

}

TY - JOUR

AU - Harvey, F. Reese

AU - Lawson, H. Blaine

TI - The restriction theorem for fully nonlinear subequations

JO - Annales de l’institut Fourier

PY - 2014

PB - Association des Annales de l’institut Fourier

VL - 64

IS - 1

SP - 217

EP - 265

AB - Let $X$ be a submanifold of a manifold $Z$. We address the question: When do viscosity subsolutions of a fully nonlinear PDE on $Z$, restrict to be viscosity subsolutions of the restricted subequation on $X$? This is not always true, and conditions are required. We first prove a basic result which, in theory, can be applied to any subequation. Then two definitive results are obtained. The first applies to any “geometrically defined” subequation, and the second to any subequation which can be transformed to a constant coefficient (i.e., euclidean) model. This provides a long list of geometrically and analytically interesting cases where restriction holds.

LA - eng

KW - Viscosity solution; viscosity subsolution; nonlinear second-order elliptic equations; restriction; submanifold; pluripotential theory; viscosity solution

UR - http://eudml.org/doc/275604

ER -

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