Concentration compactness principle at infinity with partial symmetry and its application

Michinori Ishiwata, Mitsuharu Otani

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    The concentration compactness problem (CCP), which plays a very important role in the study of nonlinear partial differential equations and nonlinear eliiptic equations, was studied. The partial symmetry of the problem at infinity was analyzed. The partial symmetry of the domain was formulated in terms of the transformation group acting on the domain. Some semilinear elliptic equations in the infinite cylindrical domains with axial symmetry were discussed to illustrate the applicability of the results.

    Original languageEnglish
    Pages (from-to)391-407
    Number of pages17
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume51
    Issue number3
    DOIs
    Publication statusPublished - 2002 Nov

    Fingerprint

    Concentration-compactness Principle
    Nonlinear equations
    Partial differential equations
    Infinity
    Partial
    Symmetry
    Concentration-compactness
    Axial Symmetry
    Transformation group
    Semilinear Elliptic Equations
    Nonlinear Partial Differential Equations
    Nonlinear Equations

    Keywords

    • Concentration compactness principle
    • Infinite cylindrical domain
    • Partial symmetry
    • Supercritical nonlinearity

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Mathematics(all)

    Cite this

    Concentration compactness principle at infinity with partial symmetry and its application. / Ishiwata, Michinori; Otani, Mitsuharu.

    In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 51, No. 3, 11.2002, p. 391-407.

    Research output: Contribution to journalArticle

    @article{855b5b8c88294e918a2da309a4ae3748,
    title = "Concentration compactness principle at infinity with partial symmetry and its application",
    abstract = "The concentration compactness problem (CCP), which plays a very important role in the study of nonlinear partial differential equations and nonlinear eliiptic equations, was studied. The partial symmetry of the problem at infinity was analyzed. The partial symmetry of the domain was formulated in terms of the transformation group acting on the domain. Some semilinear elliptic equations in the infinite cylindrical domains with axial symmetry were discussed to illustrate the applicability of the results.",
    keywords = "Concentration compactness principle, Infinite cylindrical domain, Partial symmetry, Supercritical nonlinearity",
    author = "Michinori Ishiwata and Mitsuharu Otani",
    year = "2002",
    month = "11",
    doi = "10.1016/S0362-546X(01)00836-7",
    language = "English",
    volume = "51",
    pages = "391--407",
    journal = "Nonlinear Analysis, Theory, Methods and Applications",
    issn = "0362-546X",
    publisher = "Elsevier Limited",
    number = "3",

    }

    TY - JOUR

    T1 - Concentration compactness principle at infinity with partial symmetry and its application

    AU - Ishiwata, Michinori

    AU - Otani, Mitsuharu

    PY - 2002/11

    Y1 - 2002/11

    N2 - The concentration compactness problem (CCP), which plays a very important role in the study of nonlinear partial differential equations and nonlinear eliiptic equations, was studied. The partial symmetry of the problem at infinity was analyzed. The partial symmetry of the domain was formulated in terms of the transformation group acting on the domain. Some semilinear elliptic equations in the infinite cylindrical domains with axial symmetry were discussed to illustrate the applicability of the results.

    AB - The concentration compactness problem (CCP), which plays a very important role in the study of nonlinear partial differential equations and nonlinear eliiptic equations, was studied. The partial symmetry of the problem at infinity was analyzed. The partial symmetry of the domain was formulated in terms of the transformation group acting on the domain. Some semilinear elliptic equations in the infinite cylindrical domains with axial symmetry were discussed to illustrate the applicability of the results.

    KW - Concentration compactness principle

    KW - Infinite cylindrical domain

    KW - Partial symmetry

    KW - Supercritical nonlinearity

    UR - http://www.scopus.com/inward/record.url?scp=0036833054&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0036833054&partnerID=8YFLogxK

    U2 - 10.1016/S0362-546X(01)00836-7

    DO - 10.1016/S0362-546X(01)00836-7

    M3 - Article

    VL - 51

    SP - 391

    EP - 407

    JO - Nonlinear Analysis, Theory, Methods and Applications

    JF - Nonlinear Analysis, Theory, Methods and Applications

    SN - 0362-546X

    IS - 3

    ER -