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Volumn 224, Issue , 2001, Pages 75-104

Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions

Author keywords

( , ) domain; Dirichlet form; Douglas integral; Reflecting diffusion; Subordination in the sense of Bochner; Trace operator; Weyl decomposition

Indexed keywords


EID: 0037907017     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200104)224:1<75::AID-MANA75>3.0.CO;2-N     Document Type: Article
Times cited : (28)

References (63)
  • 2
    • 0039759936 scopus 로고
    • Traces of potentials arising from translation invariant operators
    • ADAMS, D. R.: Traces of Potentials Arising from Translation Invariant Operators, Ann. Sc. Norm. Sup. Pisa 25 (1971), 203-217
    • (1971) Ann. Sc. Norm. Sup. Pisa , vol.25 , pp. 203-217
    • Adams, D.R.1
  • 5
    • 0039759950 scopus 로고
    • Birkhäuser, Basel
    • AMANN, H.: Linear and Quasi-Linear Parabolic Problems, Vol. I Abstract Linear Theory, Monographs in Mathematics Vol. 89, Birkhäuser, Basel, 1995
    • (1995) Monographs in Mathematics , vol.89
  • 6
    • 84972506990 scopus 로고
    • Fractional powers of closed operators and semigroups generated by them
    • BALAKRISHNAN, A. V.: Fractional Powers of Closed Operators and Semigroups Generated by Them, Pacific J. Math. 10 (1960), 419-437
    • (1960) Pacific J. Math. , vol.10 , pp. 419-437
    • Balakrishnan, A.V.1
  • 7
    • 0039269962 scopus 로고
    • The semimartingale structure of reflecting brownian motion
    • BASS, R. F., and Hsu, P. E.: The Semimartingale Structure of Reflecting Brownian Motion, Proc. Amer. Math. Soc. 108 (1990), 1007-1010
    • (1990) Proc. Amer. Math. Soc. , vol.108 , pp. 1007-1010
    • Bass, R.F.1    Hsu, P.E.2
  • 8
    • 0001584203 scopus 로고
    • Some potential theory for reflecting brownian motion in hölder and lipschitz domains
    • BASS, R. F., and Hsu, P. E.: Some Potential Theory for Reflecting Brownian Motion in Hölder and Lipschitz Domains, Ann. Prob. 19 (1991), 486-508
    • (1991) Ann. Prob. , vol.19 , pp. 486-508
    • Bass, R.F.1    Hsu, P.E.2
  • 11
    • 0000719476 scopus 로고
    • Diffusion equation and stochastic processes
    • BOCHNER, S.: Diffusion Equation and Stochastic Processes, Proc. Natl. Acad. Sci. 35 (1949), 368-370
    • (1949) Proc. Natl. Acad. Sci. , vol.35 , pp. 368-370
    • Bochner, S.1
  • 12
    • 0003534689 scopus 로고
    • Harmonic analysis and the theory of probability
    • University of California Press, Berkeley CA
    • BOCHNER, S.: Harmonic Analysis and the Theory of Probability, California Monographs in Math. Sci., University of California Press, Berkeley CA, 1955
    • (1955) California Monographs in Math. Sci.
    • Bochner, S.1
  • 13
    • 0034360422 scopus 로고    scopus 로고
    • Approximation by functions of compact support in besov-triebel-lizorkin spaces on irregular domains
    • CAETANO, A.: Approximation by Functions of Compact Support in Besov-Triebel-Lizorkin Spaces on Irregular Domains, Studia Math. 142 (2000), 47-63
    • (2000) Studia Math. , vol.142 , pp. 47-63
    • Caetano, A.1
  • 14
    • 0003152974 scopus 로고
    • Misure e Integrazione sugli Insiemi Dimesionalmente Orientati
    • CACCIOPOLI, R.: Misure e Integrazione sugli Insiemi Dimesionalmente Orientati, Rend. Accad. Naz. dei Lincei 12 (1953), 3-11, 137-146
    • (1953) Rend. Accad. Naz. Dei Lincei , vol.12 , pp. 3-11
    • Cacciopoli, R.1
  • 15
    • 0001170037 scopus 로고
    • Reflecting brownian motions: Quasimartingales and strong cacciopoli sets
    • CHEN, Z. Q., FITZSIMMONS, P. J., and WILLIAMS, R. J.: Reflecting Brownian Motions: Quasimartingales and Strong Cacciopoli Sets, Potential Analysis 2 (1993), 219-243
    • (1993) Potential Analysis , vol.2 , pp. 219-243
    • Chen, Z.Q.1    Fitzsimmons, P.J.2    Williams, R.J.3
  • 16
    • 0000245505 scopus 로고
    • Su una Teoria Generale della Misure (r - 1) Dimensionale in uno Spazio ad r Dimensioni
    • DE GIORGI, E.: Su una Teoria Generale della Misure (r - 1) Dimensionale in uno Spazio ad r Dimensioni, Ann. Mat. Pura Appl. IV Ser. 36 (1954), 191-213
    • (1954) Ann. Mat. Pura Appl. IV Ser. , vol.36 , pp. 191-213
    • De Giorgi, E.1
  • 17
    • 0001844148 scopus 로고
    • Nuovi Teoremi Relative alle Misure (r - 1) Dimensionale in Spazio ad r Dimensioni
    • DE GIORGI, E.: Nuovi Teoremi Relative alle Misure (r - 1) Dimensionale in Spazio ad r Dimensioni, Ric. Mat. 4 (1955), 95-113
    • (1955) Ric. Mat. , vol.4 , pp. 95-113
    • De Giorgi, E.1
  • 19
    • 33750322857 scopus 로고
    • Linear operators I
    • Interscience Publishers, New York
    • DUNFORD, N., and SCHWARTZ, J. T.: Linear Operators I, Pure Appl. Math. Vol. 7, Interscience Publishers, New York, 1957
    • (1957) Pure Appl. Math. , vol.7
    • Dunford, N.1    Schwartz, J.T.2
  • 22
    • 0039261467 scopus 로고
    • Extensions from anisotropic sobolev spaces
    • in Russian
    • FAJN, B. L.: Extensions from Anisotropic Sobolev Spaces, Trudy Math. Inst. Steklov 158 (1984), 248-273 (in Russian)
    • (1984) Trudy Math. Inst. Steklov , vol.158 , pp. 248-273
    • Fajn, B.L.1
  • 27
    • 0002319407 scopus 로고
    • A discrete transform and decomposition of distribution spaces
    • FRAZIER, M., and JAWERTH, B.: A Discrete Transform and Decomposition of Distribution Spaces, J. Funct. Anal. 93 (1990), 34-170
    • (1990) J. Funct. Anal. , vol.93 , pp. 34-170
    • Frazier, M.1    Jawerth, B.2
  • 28
    • 0039167419 scopus 로고    scopus 로고
    • Dirichlet forms, cacciopoli sets and the skorohod representation
    • CSISZAR, MICHALETZKY (eds), Birkhäuser Verlag, Basel
    • FUKUSHIMA, M.: Dirichlet Forms, Cacciopoli Sets and the Skorohod Representation. In: CSISZAR, MICHALETZKY (eds), Stochastic Differential and Difference Equations, pp. 59-66, Birkhäuser Verlag, Basel, 1997
    • (1997) Stochastic Differential and Difference Equations , pp. 59-66
    • Fukushima, M.1
  • 29
    • 0040351952 scopus 로고    scopus 로고
    • Decompositions of symmetric diffusions and related topics in analysis
    • in Japanese
    • FUKUSHIMA, M.: Decompositions of Symmetric Diffusions and Related Topics in Analysis, Sugaku 50 (1998), 56-67 (in Japanese)
    • (1998) Sugaku , vol.50 , pp. 56-67
    • Fukushima, M.1
  • 31
    • 0011770714 scopus 로고
    • Reflecting diffusions on lipschitz domains with cusps -analytic construction and skorohod representation
    • FUKUSHIMA, M., and TOMISAKI, M.: Reflecting Diffusions on Lipschitz Domains with Cusps -Analytic Construction and Skorohod Representation, Potential Analysis 4 (1995), 377-408
    • (1995) Potential Analysis , vol.4 , pp. 377-408
    • Fukushima, M.1    Tomisaki, M.2
  • 32
    • 0040955144 scopus 로고    scopus 로고
    • Construction and decomposition of reflecting diffusions on lipschitz domains with hölder cusps
    • FUKUSHIMA, M., and TOMISAKI, M.: Construction and Decomposition of Reflecting Diffusions on Lipschitz Domains with Hölder Cusps, Probab. Theory Relat. Fields 106 (1996), 521-557
    • (1996) Probab. Theory Relat. Fields , vol.106 , pp. 521-557
    • Fukushima, M.1    Tomisaki, M.2
  • 33
    • 0003343498 scopus 로고
    • Minimal surfaces and functions of bounded variation
    • Birkhäuser Verlag
    • GIUSTI, E.: Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics Vol. 80, Birkhäuser Verlag, 1984
    • (1984) Monographs in Mathematics , vol.80
    • Giusti, E.1
  • 34
    • 0039323064 scopus 로고
    • Domaines d'Opérateurs Représentés comme Intégrales de Resolvantes
    • HIRSCH, F.: Domaines d'Opérateurs Représentés comme Intégrales de Resolvantes, J. Funct. Anal. 23 (1976), 239-264
    • (1976) J. Funct. Anal. , vol.23 , pp. 239-264
    • Hirsch, F.1
  • 35
    • 0040351946 scopus 로고
    • Extension des Propriétés des Puissances Fractionaires
    • Sém. Theorie du Potentiel, Springer-Verlag, Berlin
    • HIRSCH, F.: Extension des Propriétés des Puissances Fractionaires. In: Sém. Theorie du Potentiel, Lecture Notes in Mathematics Vol. 563, pp. 100-120, Springer-Verlag, Berlin 1976
    • (1976) Lecture Notes in Mathematics , vol.563 , pp. 100-120
    • Hirsch, F.1
  • 37
    • 0033483059 scopus 로고    scopus 로고
    • Some dirichlet spaces obtained by subordinate reflected diffusions
    • JACOB, N., and SCHILLING, R. L.: Some Dirichlet Spaces Obtained by Subordinate Reflected Diffusions, Rev. Math. Iberoamericana 15 (1999), 59-91
    • (1999) Rev. Math. Iberoamericana , vol.15 , pp. 59-91
    • Jacob, N.1    Schilling, R.L.2
  • 38
    • 0002004980 scopus 로고
    • Boundary behavior of harmonic functions in nontangentially accessible domains
    • JERISON, D., and KENIG, C.: Boundary Behavior of Harmonic Functions in Nontangentially Accessible Domains, Adv. Math. 46 (1982), 80-146
    • (1982) Adv. Math. , vol.46 , pp. 80-146
    • Jerison, D.1    Kenig, C.2
  • 39
    • 0002428795 scopus 로고
    • Quasiconformal mappings and extendability of functions in sobolev spaces
    • JONES, P. W.: Quasiconformal Mappings and Extendability of Functions in Sobolev Spaces, Acta Math. 147 (1981), 71-88
    • (1981) Acta Math. , vol.147 , pp. 71-88
    • Jones, P.W.1
  • 41
  • 42
    • 0040945975 scopus 로고    scopus 로고
    • Boundary value problems and brownian motion on fractals, chaos
    • JONSSON, A., and WALLIN, H.: Boundary Value Problems and Brownian Motion on Fractals, Chaos, Solitons and Fractals 8 (1997), 191-205
    • (1997) Solitons and Fractals , vol.8 , pp. 191-205
    • Jonsson, A.1    Wallin, H.2
  • 43
    • 0039167418 scopus 로고
    • The trace of sobolev-slobodeckij spaces on lipschitz domains
    • MARSCHALL, J.: The Trace of Sobolev-Slobodeckij Spaces on Lipschitz Domains, Manuscripta Math. 58 (1987), 47-65
    • (1987) Manuscripta Math. , vol.58 , pp. 47-65
    • Marschall, J.1
  • 46
    • 84972536281 scopus 로고
    • On the generation of semigroups of linear operators
    • PHILLIPS, R. S.: On the Generation of Semigroups of Linear Operators, Pacific J. Math. 2 (1952), 343-369
    • (1952) Pacific J. Math. , vol.2 , pp. 343-369
    • Phillips, R.S.1
  • 48
    • 0013064873 scopus 로고    scopus 로고
    • On the domain of the generator of a subordinate semigroup
    • L. KRAL et al (eds), Potential Theory - ICTP 94, Walter de Gruyter Verlag, Berlin
    • SCHILLING, R. L.: On the Domain of the Generator of a Subordinate Semigroup. In: L. KRAL et al (eds), Potential Theory - ICTP 94, Proceedings Int. Conf. Potential Theory, Kouty (CR), 1994, pp. 446-462, Walter de Gruyter Verlag, Berlin, 1996
    • (1996) Proceedings Int. Conf. Potential Theory, Kouty (CR), 1994 , pp. 446-462
    • Schilling, R.L.1
  • 49
    • 0040350238 scopus 로고    scopus 로고
    • Subordination in the sense of bochner and a related functional calculus
    • SCHILLING, R. L.: Subordination in the Sense of Bochner and a Related Functional Calculus, J. Austral. Math. Soc. (Ser. A) 64 (1998), 368-396
    • (1998) J. Austral. Math. Soc. (Ser. A) , vol.64 , pp. 368-396
    • Schilling, R.L.1
  • 50
  • 51
    • 0002597257 scopus 로고
    • p with boundary conditions
    • p with Boundary Conditions, Studia Math. 44 (1972), 47-60
    • (1972) Studia Math. , vol.44 , pp. 47-60
    • Seeley, R.1
  • 59
    • 0000344624 scopus 로고    scopus 로고
    • A fourier analytical characterization of the hausdorff dimension of a closed set and of related lebesgue spaces
    • TRIEBEL, H., and WINKELVOSS, H.: A Fourier Analytical Characterization of the Hausdorff Dimension of a Closed Set and of Related Lebesgue Spaces, Studia Math. 121 (1996), 149-166
    • (1996) Studia Math. , vol.121 , pp. 149-166
    • Triebel, H.1    Winkelvoss, H.2
  • 61
    • 51249175101 scopus 로고
    • The trace to the boundary of sobolev spaces on a snowflake
    • WALLIN, H.: The Trace to the Boundary of Sobolev Spaces on a Snowflake, Manuscripta Math. 73 (1991), 117-125
    • (1991) Manuscripta Math. , vol.73 , pp. 117-125
    • Wallin, H.1


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