메뉴 건너뛰기




Volumn 35, Issue 11, 2010, Pages 2092-2122

Extension problem and Harnack's inequality for some fractional operators

Author keywords

Degenerate schr dinger equation; Fractional laplacian; Harmonic oscillator; Harnack's inequality; Heat semigroup

Indexed keywords


EID: 77957945365     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605301003735680     Document Type: Article
Times cited : (516)

References (14)
  • 1
    • 37849049246 scopus 로고    scopus 로고
    • Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
    • Caffarelli, L., Salsa, S., Silvestre, L. (2008). Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Invent. Math. 171:425-461.
    • (2008) Invent. Math. , vol.171 , pp. 425-461
    • Caffarelli, L.1    Salsa, S.2    Silvestre, L.3
  • 2
    • 34548348805 scopus 로고    scopus 로고
    • An extension problem related to the fractional Laplacian
    • Caffarelli, L., Silvestre, L. (2007). An extension problem related to the fractional Laplacian. Comm. Part. Diff. Eqs. 32:1245-1260.
    • (2007) Comm. Part. Diff. Eqs. , vol.32 , pp. 1245-1260
    • Caffarelli, L.1    Silvestre, L.2
  • 3
    • 0003287060 scopus 로고
    • Heat Kernels and Spectral Theory
    • Cambridge: Cambridge University Press
    • Davies, E.B. (1989). Heat Kernels and Spectral Theory. Cambrigde Tracts in Mathematics. Vol. 92. Cambridge: Cambridge University Press.
    • (1989) Cambrigde Tracts in Mathematics , vol.92
    • Davies, E.B.1
  • 4
    • 0001601186 scopus 로고
    • Harnack's inequality for degenerate Schrödinger operators
    • Gutiérrez, C.E. (1989). Harnack's inequality for degenerate Schrödinger operators. Trans. Amer. Math. Soc. 312:403-419.
    • (1989) Trans. Amer. Math. Soc. , vol.312 , pp. 403-419
    • Gutiérrez, C.E.1
  • 5
    • 1842486135 scopus 로고    scopus 로고
    • p-dimension free boundedness for Riesz transforms associated to Hermite functions
    • p-dimension free boundedness for Riesz transforms associated to Hermite functions. Math. Ann. 328:653-682.
    • (2004) Math. Ann. , vol.328 , pp. 653-682
    • Harboure, E.1    de Rosa, L.2    Segovia, C.3    Torrea, J.L.4
  • 7
    • 84968515925 scopus 로고
    • Classical expansions and their relation to conjugate harmonic functions
    • Muckenhoupt, B., Stein, E.M. (1965). Classical expansions and their relation to conjugate harmonic functions. Trans. Amer. Math. Soc. 118:17-92.
    • (1965) Trans. Amer. Math. Soc. , vol.118 , pp. 17-92
    • Muckenhoupt, B.1    Stein, E.M.2
  • 10
    • 33751514593 scopus 로고    scopus 로고
    • Regularity of the obstacle problem for a fractional power of the Laplace operator
    • Silvestre, L. (2007). Regularity of the obstacle problem for a fractional power of the Laplace operator. Comm. Pure Appl. Math. 60:67-112.
    • (2007) Comm. Pure Appl. Math. , vol.60 , pp. 67-112
    • Silvestre, L.1
  • 11
    • 0001964876 scopus 로고
    • Topics in Harmonic analysis related to the littlewood-paley theory
    • Princeton, NJ: Princeton University Press
    • Stein, E.M. (1970). Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Annals of Mathematics Studies, Vol. 63. Princeton, NJ: Princeton University Press.
    • (1970) Annals of Mathematics Studies , vol.63
    • Stein, E.M.1
  • 12
    • 0003244651 scopus 로고
    • Lectures on Hermite and laguerre expansions
    • Princeton, NJ: Princeton University Press
    • Thangavelu, S. (1993). Lectures on Hermite and Laguerre Expansions. Mathematical Notes, Vol. 42. Princeton, NJ: Princeton University Press.
    • (1993) Mathematical Notes , vol.42
    • Thangavelu, S.1
  • 13
    • 0006027422 scopus 로고
    • Linear elliptic operators with measurable coefficients
    • Trudinger, N.S. (1973). Linear elliptic operators with measurable coefficients. Ann. Scuola Norm. Sup. Pisa 27:265-308.
    • (1973) Ann. Scuola Norm. Sup. Pisa , vol.27 , pp. 265-308
    • Trudinger, N.S.1
  • 14
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • Zaslavsky, G.M. (2002). Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371:461-580.
    • (2002) Phys. Rep. , vol.371 , pp. 461-580
    • Zaslavsky, G.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.