# Energy quantization and mean value inequalities for nonlinear boundary value problems

Journal of the European Mathematical Society (2005)

- Volume: 007, Issue: 3, page 305-318
- ISSN: 1435-9855

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topWehrheim, Katrin. "Energy quantization and mean value inequalities for nonlinear boundary value problems." Journal of the European Mathematical Society 007.3 (2005): 305-318. <http://eudml.org/doc/277664>.

@article{Wehrheim2005,

abstract = {We give a unified statement and proof of a class of well known mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energy quantization principle for sequences of solutions of boundary
value problems that have bounded energy and whose energy densities satisfy nonlinear bounds on the Laplacian and normal derivative: One obtains local uniform bounds on the complement of
finitely many points, where some minimum quantum of energy concentrates.},

author = {Wehrheim, Katrin},

journal = {Journal of the European Mathematical Society},

keywords = {variational methods; extremal problems; energy quantization principle},

language = {eng},

number = {3},

pages = {305-318},

publisher = {European Mathematical Society Publishing House},

title = {Energy quantization and mean value inequalities for nonlinear boundary value problems},

url = {http://eudml.org/doc/277664},

volume = {007},

year = {2005},

}

TY - JOUR

AU - Wehrheim, Katrin

TI - Energy quantization and mean value inequalities for nonlinear boundary value problems

JO - Journal of the European Mathematical Society

PY - 2005

PB - European Mathematical Society Publishing House

VL - 007

IS - 3

SP - 305

EP - 318

AB - We give a unified statement and proof of a class of well known mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energy quantization principle for sequences of solutions of boundary
value problems that have bounded energy and whose energy densities satisfy nonlinear bounds on the Laplacian and normal derivative: One obtains local uniform bounds on the complement of
finitely many points, where some minimum quantum of energy concentrates.

LA - eng

KW - variational methods; extremal problems; energy quantization principle

UR - http://eudml.org/doc/277664

ER -

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