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Volumn 175, Issue 1, 1998, Pages 59-91

Some interpolation inequalities involving stokes operator and first order derivatives

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EID: 33845223403     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF01783676     Document Type: Article
Times cited : (13)

References (55)
  • 1
    • 84972498579 scopus 로고
    • Problems isopérimétriques et espaces de Sobolev
    • TH. AUBIN, Problems isopérimétriques et espaces de Sobolev, J. Diff. Geom., 11 (1976), pp. 573-598
    • (1976) J. Diff. Geom. , vol.11 , pp. 573-598
    • Aubin, T.H.1
  • 3
    • 0001088288 scopus 로고
    • Algebraic L2 decay for Navier-Stokes floivs in exterior domains
    • W. BORCHERS - T. MIYAKAWA, Algebraic L2 decay for Navier-Stokes floivs in exterior domains, Acta Mathem., 165 (1990), pp. 189-227.
    • (1990) Acta Mathem. , vol.165 , pp. 189-227
    • Borchers, W.1    Miyakawa, T.2
  • 4
    • 0000927436 scopus 로고
    • First order interpolation inequalities unth weights
    • L. CAFFARELLI - R. KOHN - L. NIRENBERG, First order interpolation inequalities unth weights, Compos. Math., 39 (1984), pp. 259-275.
    • (1984) Compos. Math. , vol.39 , pp. 259-275
    • Caffarelli, L.1    Kohn, R.2    Nirenberg, L.3
  • 5
    • 0001663212 scopus 로고
    • Su im problema al contorno relativo al sistema di equazioni di Stokes
    • L. CATTABRIGA, Su im problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova, 31 (1961), pp. 308-340.
    • (1961) Rend. Sem. Mat. Univ. Padova , vol.31 , pp. 308-340
    • Cattabriga, L.1
  • 7
    • 33646917618 scopus 로고
    • A new proof of Moser's parabolic Harnark inequality via the old ideas of Nash
    • E. B. FABES - D. W. STROOK, A new proof of Moser's parabolic Harnark inequality via the old ideas of Nash, Arch. Rational Mech. Anal., 96 (1986), pp. 327-338.
    • (1986) Arch. Rational Mech. Anal. , vol.96 , pp. 327-338
    • Fabes, E.B.1    Strook, D.W.2
  • 8
    • 34250947482 scopus 로고
    • On the Navier-Stokes initial value problem
    • H. FUJITA - T. KATO, On the Navier-Stokes initial value problem, Arch. Rational Mech. Anal., 16 (1964), pp. 269-315.
    • (1964) Arch. Rational Mech. Anal. , vol.16 , pp. 269-315
    • Fujita, H.1    Kato, T.2
  • 10
    • 0001092506 scopus 로고
    • Propriété di alcune classi difunzioni in più variabili
    • E. GAGLIARDO, Propriété di alcune classi difunzioni in più variabili, Ricerche Mat. Univ. Napoli, 7 (1958), pp. 102-137.
    • (1958) Ricerche Mat. Univ. Napoli , vol.7 , pp. 102-137
    • Gagliardo, E.1
  • 11
    • 0002538288 scopus 로고
    • Ulteriori proprietà di alcune classi di funzioni in più variabili
    • E. GAGLIARDO, Ulteriori proprietà di alcune classi di funzioni in più variabili, Ricerche Mat. Univ. Napoli, 8 (1959), pp. 24-51.
    • (1959) Ricerche Mat. Univ. Napoli , vol.8 , pp. 24-51
    • Gagliardo, E.1
  • 12
    • 33845220244 scopus 로고
    • Caratterizazione costruttiva di tutti gli spazi di interpolazione fra spazi di Banach
    • E. GAGLIARDO, Caratterizazione costruttiva di tutti gli spazi di interpolazione fra spazi di Banach, Symposia Mathematica, 2 (1969), pp. 95-106.
    • (1969) Symposia Mathematica , vol.2 , pp. 95-106
    • Gagliardo, E.1
  • 14
    • 0001967348 scopus 로고
    • Monotonie decreasing and asymptotic behavoir of the kinetic energy for iveak solutions of the Navier-Stokes equations in exterior domains
    • G. P. GALDI - P. MAREMONTI, Monotonie decreasing and asymptotic behavoir of the kinetic energy for iveak solutions of the Navier-Stokes equations in exterior domains, Arch. Rational Mech. Anal., 94 (1986), pp. 253-266.
    • (1986) Arch. Rational Mech. Anal. , vol.94 , pp. 253-266
    • Galdi P Maremonti, G.P.1
  • 15
    • 0001418805 scopus 로고
    • Existence, uniqueness and L? estimates for the Stokes problem in an exterior domain
    • G. P. GALDI - C. G. SIMADER, Existence, uniqueness and L? estimates for the Stokes problem in an exterior domain, Arch. Rational Mech. Anal., 112 (1990), pp. 291-318.
    • (1990) Arch. Rational Mech. Anal. , vol.112 , pp. 291-318
    • Galdi, G.P.1    Simader, C.G.2
  • 16
    • 0000499081 scopus 로고
    • On the Stokes operator in exterior domains
    • Univ. Tokyo
    • Y. GIGA - H. SOHR, On the Stokes operator in exterior domains, J. Fac. Sci. Univ. Tokyo, 36 (1989), pp. 103-130.
    • (1989) J. Fac. Sci. , vol.36 , pp. 103-130
    • Giga, Y.1    Sohr, H.2
  • 17
    • 33845198290 scopus 로고
    • Dokl. Akad. Nauk SSSR
    • K. K. GOLOVKIN, On embedding theorems, Dokl. Akad. Nauk SSSR, 134 (1960), pp. 19-22.
    • (1960) On Embedding Theorems , vol.134 , pp. 19-22
    • Golovkin, K.K.1
  • 18
    • 0000509826 scopus 로고
    • The Navier-Stokes equations: On the existence, regularity and decay of solutions
    • J. H. HEYWOOD, The Navier-Stokes equations: on the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), pp. 639-681.
    • (1980) Indiana Univ. Math. J. , vol.29 , pp. 639-681
    • Heywood, J.H.1
  • 19
    • 33846852127 scopus 로고
    • Certain inequalities in function spaces and their application to the analysis of convergence in variational processes
    • V. P. IL'IN, Certain inequalities in function spaces and their application to the analysis of convergence in variational processes, Trudy Mat. Inst. Steklov, 66 (1959), pp. 64-127
    • (1959) Trudy Mat. Inst. Steklov , vol.66 , pp. 64-127
    • Il'In, V.P.1
  • 21
    • 0002775916 scopus 로고
    • New a priori estimates for the Stokes equations in exterior domains
    • H. KOZONO - H. SOHR, New a priori estimates for the Stokes equations in exterior domains, Indiana Univ. Math. J., 40 (1991), pp. 1-28.
    • (1991) Indiana Univ. Math. J. , vol.40 , pp. 1-28
    • Kozono, H.1    Sohr, H.2
  • 22
    • 84980079701 scopus 로고
    • Solution in large of the nonstationary boundary value problem for the Navier-Stokes system with two space variables
    • 0. A. LADYZHENSKAYA, Solution in large of the nonstationary boundary value problem for the Navier-Stokes system with two space variables, Comm. Pure Appl. Math., 12 (1959), pp. 427-433.
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 427-433
    • Ladyzhenskaya, A.1
  • 24
    • 0001950989 scopus 로고
    • Espaces intermédiaires entre espaces hilbertiens et applications
    • J. L. LIONS, Espaces intermédiaires entre espaces hilbertiens et applications, Bull. Math. Soc. Math. Phys. Roumanie, 50 (1958), pp.419-432.
    • (1958) Bull. Math. Soc. Math. Phys. Roumanie , vol.50 , pp. 419-432
    • Lions, J.L.1
  • 25
    • 0000065136 scopus 로고
    • Thérèmes de trace et d'interpolation: I-V
    • J. L. LIONS, Thérèmes de trace et d'interpolation: I-V, Ann. Se. Norm. Sup. Pisa, 13 (1959), pp. 389-403;
    • (1959) Ann. Se. Norm. Sup. Pisa , vol.13 , pp. 389-403
    • Lions, J.L.1
  • 27
    • 27544481251 scopus 로고
    • J. Math. Pures Appl., 42 (1963), pp. 195-203;
    • (1963) J. Math. Pures Appl. , vol.42 , pp. 195-203
  • 28
    • 27844548422 scopus 로고
    • Math. Annal., 151 (1963), pp. 42-56;
    • (1963) Math. Annal. , vol.151 , pp. 42-56
  • 30
    • 33845221896 scopus 로고
    • Properties of some interpolation spaces
    • J. L. LIONS, Properties of some interpolation spaces, J. Rat. Mech., 11 (1962), pp. 969-978.
    • (1962) J. Rat. Mech. , vol.11 , pp. 969-978
    • Lions, J.L.1
  • 33
    • 53149133024 scopus 로고
    • On the Existence and Pointiuise Stability of Periodic Solutions to a Linear Parabolic Equation in Unbounded Domains
    • P. MAREMONTI - R. Russo, On the Existence and Pointiuise Stability of Periodic Solutions to a Linear Parabolic Equation in Unbounded Domains, Appl. Analisys, Gordon Breach, 44 (1992).
    • (1992) Appl. Analisys, Gordon Breach , vol.44
    • Maremonti, P.1    Russo, R.2
  • 34
    • 53149118459 scopus 로고
    • Estimates of the solution of the Dirichlet problem for the Laplace operator in exterior domains, Zap
    • (in Russian)
    • P. MAREMONTI - V. A. SOLONNIKOV, Estimates of the solution of the Dirichlet problem for the Laplace operator in exterior domains, Zap. Nauch. Sem. LOMI, 180 (1985), pp. 92-101 (in Russian);
    • (1985) Nauch. Sem. LOMI , vol.180 , pp. 92-101
    • Maremonti, P.1    Solonnikov, V.A.2
  • 35
    • 33845232562 scopus 로고
    • J. Soviet Math., 40 (1988), pp. 72-79.
    • (1988) J. Soviet Math. , vol.40 , pp. 72-79
  • 36
    • 0042104729 scopus 로고
    • An estimate for solutions of the Stokes system in exterior domains
    • (in Russian)
    • P. MAREMONTI - V. A. SOLONNIKOV, An estimate for solutions of the Stokes system in exterior domains, Zap. Nauch. Sem. LOMI, 180 (1990), pp. 105-120 (in Russian);
    • (1990) Zap. Nauch. Sem. LOMI , vol.180 , pp. 105-120
    • Maremonti, P.1    Solonnikov, V.A.2
  • 37
    • 0346832205 scopus 로고
    • J. Math. Sci., 68 (1994), pp. 229-239.
    • (1994) J. Math. Sci. , vol.68 , pp. 229-239
  • 39
    • 84972520515 scopus 로고
    • On the stability of incompressible viscous fluid motions past objects
    • Japan
    • K. MASUDA, On the stability of incompressible viscous fluid motions past objects, J. Math. Soc. Japan, 27 (1975), pp. 294-327.
    • (1975) J. Math. Soc. , vol.27 , pp. 294-327
    • Masuda, K.1
  • 40
    • 33845218415 scopus 로고
    • Su alcune diseguaglianze integrali
    • C. MIRANDA, Su alcune diseguaglianze integrali, Mem. Ace. Lincei, 7 (1963), pp. 1-14.
    • (1963) Mem. Ace. Lincei , vol.7 , pp. 1-14
    • Miranda, C.1
  • 41
    • 24044479200 scopus 로고
    • Su alcuni teoremi di indusione
    • C. MIRANDA, Su alcuni teoremi di indusione, Annales Polonici Math., 16 (1965), pp. 305-315.
    • (1965) Annales Polonici Math. , vol.16 , pp. 305-315
    • Miranda, C.1
  • 42
    • 0009880314 scopus 로고
    • Istituzioni di analisi funzionale lineare
    • C. MIRANDA, Istituzioni di analisi funzionale lineare, U.M.I., Oderisi, Gubbio, 1 (1978).
    • (1978) U.M.I., Oderisi, Gubbio , vol.1
    • Miranda, C.1
  • 43
    • 0001680091 scopus 로고
    • Continuity of solutions of parabolic and elliptic equations
    • J. NASH, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math, 80 (1958), pp. 931-954.
    • (1958) Amer. J. Math , vol.80 , pp. 931-954
    • Nash, J.1
  • 44
    • 0000973918 scopus 로고
    • On elliptic partial differential equations
    • L. NIRENBERG, On elliptic partial differential equations, Ann. Sc. Norm. Sup. Pisa, 13 (1959), pp. 123-131.
    • (1959) Ann. Sc. Norm. Sup. Pisa , vol.13 , pp. 123-131
    • Nirenberg, L.1
  • 45
    • 0001702448 scopus 로고
    • An extended interpolation inequality
    • L. NlRENBERG, An extended interpolation inequality, Ann. Sc. Norm. Sup. Pisa, 20 (1966), pp. 733-737.
    • (1966) Ann. Sc. Norm. Sup. Pisa , vol.20 , pp. 733-737
    • Nlrenberg, L.1
  • 46
    • 0003183559 scopus 로고
    • A non-inequality for differential operators in the Ll norm
    • D. ORNSTEIN, A non-inequality for differential operators in the Ll norm, Arch. Rational Mech. Anal., 11 (1962), pp. 40-49.
    • (1962) Arch. Rational Mech. Anal. , vol.11 , pp. 40-49
    • Ornstein, D.1
  • 47
    • 0011331696 scopus 로고    scopus 로고
    • The Helmkoltz decomposition in Lq and related topics, in Mathematical Problems Related to the Navier-Stokes equations
    • G. P. Galdi Ed., (World Scientific)
    • C. G. SIMADER - H. SOHR, The Helmkoltz decomposition in Lq and related topics, in Mathematical Problems Related to the Navier-Stokes equations, G. P. Galdi Ed., Advances in Math. Appl. Sciences, 11 (World Scientific), pp. 1-35.
    • Advances in Math. Appl. Sciences , vol.11 , pp. 1-35
    • Simader, C.G.1    Sohr, H.2
  • 48
    • 0042096912 scopus 로고
    • On the estimates of the tensor Green's function for certain boundary problems
    • V. A SOLONNIKOV, On the estimates of the tensor Green's function for certain boundary problems, Soviet Math. Doklady, 1 (1960), pp. 128-131.
    • (1960) Soviet Math. Doklady , vol.1 , pp. 128-131
    • Solonnikov, V.A.1
  • 49
    • 33845217260 scopus 로고
    • Inequalities for functions of the class Wp(Rn)
    • V. A. SOLONNIKOV, Inequalities for functions of the class Wp(Rn), J. Soviet Math., 3 (1975), pp. 549-564.
    • (1975) J. Soviet Math. , vol.3 , pp. 549-564
    • Solonnikov, V.A.1
  • 50
    • 0037867566 scopus 로고
    • General boundary value problems for Douglis Nirenberg elliptic system H
    • V. A SOLONNIKOV, General boundary value problems for Douglis Nirenberg elliptic system H, Proc. Steklov Inst. Math., 110 (1970), pp. 123-170.
    • (1970) Proc. Steklov Inst. Math. , vol.110 , pp. 123-170
    • Solonnikov, V.A.1
  • 51
    • 34250298739 scopus 로고
    • Estimates for solutions of nonstationary Navier-Stokes equations
    • V. A SOLONNIKOV, Estimates for solutions of nonstationary Navier-Stokes equations, J. Soviet Math., 8 (1977), pp. 467-528.
    • (1977) J. Soviet Math. , vol.8 , pp. 467-528
    • Solonnikov, V.A.1
  • 52
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • G. TALENTI, Best constant in Sobolev inequality, Ann. Mat. Pura Appl., 110 (1976), pp. 353-372.
    • (1976) Ann. Mat. Pura Appl. , vol.110 , pp. 353-372
    • Talenti, G.1
  • 54
    • 0041030128 scopus 로고
    • A sharp pointwise bound for functions tvith Lz-Laplacian and zero boundary values on arbitrary three-dimensional domains
    • W. XIE, A sharp pointwise bound for functions tvith Lz-Laplacian and zero boundary values on arbitrary three-dimensional domains, Indiana Univ. Math. J., 40 (1991), pp. 1185-1192.
    • (1991) Indiana Univ. Math. J. , vol.40 , pp. 1185-1192
    • Xie, W.1
  • 55
    • 0038441036 scopus 로고
    • Fractional powers of operators, interpolation theory and embedding theorems
    • A. YOSHIKAWA, Fractional powers of operators, interpolation theory and embedding theorems, J. Fac. Sci. Univ. Tokyo, 18 (1971), pp. 335-362.
    • (1971) , J. Fac. Sci. Univ. Tokyo , vol.18 , pp. 335-362
    • Yoshikawa, A.1


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