A Comparison Theorem for Nonsmooth Nonlinear Operators

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A Comparison Theorem for Nonsmooth Nonlinear Operators. / Kozlov, Vladimir; Nazarov, Alexander.

In: Potential Analysis, Vol. 54, No. 3, 11.03.2020, p. 471-481.

Research output: Contribution to journal › Article › peer-review

Author

Kozlov, Vladimir ; Nazarov, Alexander. / A Comparison Theorem for Nonsmooth Nonlinear Operators. In: Potential Analysis. 2020 ; Vol. 54, No. 3. pp. 471-481.

BibTeX

@article{e13811d62bd240cf99a89433460560c5,

title = "A Comparison Theorem for Nonsmooth Nonlinear Operators",

abstract = "We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearity f is Lp function with p > 1. The proof is based on a strong maximum principle for solutions of divergence type elliptic equations with VMO leading coefficients and with lower order coefficients from a Kato class. An application to estimation of periodic water waves profiles is given.",

keywords = "Comparison principal, Kato classes, Non-smooth nonlinearity, Semi-linear elliptic equation, Strong maximum principle, VMO coefficients",

author = "Vladimir Kozlov and Alexander Nazarov",

note = "Publisher Copyright: {\textcopyright} 2020, The Author(s).",

year = "2020",

month = mar,

day = "11",

doi = "10.1007/s11118-020-09834-8",

language = "English",

volume = "54",

pages = "471--481",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - A Comparison Theorem for Nonsmooth Nonlinear Operators

AU - Kozlov, Vladimir

AU - Nazarov, Alexander

PY - 2020/3/11

Y1 - 2020/3/11

N2 - We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearity f is Lp function with p > 1. The proof is based on a strong maximum principle for solutions of divergence type elliptic equations with VMO leading coefficients and with lower order coefficients from a Kato class. An application to estimation of periodic water waves profiles is given.

AB - We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearity f is Lp function with p > 1. The proof is based on a strong maximum principle for solutions of divergence type elliptic equations with VMO leading coefficients and with lower order coefficients from a Kato class. An application to estimation of periodic water waves profiles is given.

KW - Comparison principal

KW - Kato classes

KW - Non-smooth nonlinearity

KW - Semi-linear elliptic equation

KW - Strong maximum principle

KW - VMO coefficients

UR - http://www.scopus.com/inward/record.url?scp=85081719920&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/b9961560-6c90-3d60-b3f4-d0f5e787a68d/

U2 - 10.1007/s11118-020-09834-8

DO - 10.1007/s11118-020-09834-8

M3 - Article

VL - 54

SP - 471

EP - 481

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 3

ER -

ID: 78517728