@article{ASNSP_1999_4_28_3_413_0, author = {Hansen, Wolfhard}, title = {Harnack inequalities for {Schr\"odinger} operators}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {413--470}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 28}, number = {3}, year = {1999}, zbl = {0940.35063}, mrnumber = {1736524}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1999_4_28_3_413_0/} }
TY - JOUR AU - Hansen, Wolfhard TI - Harnack inequalities for Schrödinger operators JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1999 DA - 1999/// SP - 413 EP - 470 VL - Ser. 4, 28 IS - 3 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1999_4_28_3_413_0/ UR - https://zbmath.org/?q=an%3A0940.35063 UR - https://www.ams.org/mathscinet-getitem?mr=1736524 LA - en ID - ASNSP_1999_4_28_3_413_0 ER -
Hansen, Wolfhard. Harnack inequalities for Schrödinger operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 3, pp. 413-470. http://www.numdam.org/item/ASNSP_1999_4_28_3_413_0/
[AS82] Brownian motion and Harnack's inequality for Schrödinger operators, Comm. Pure Appl. Math. 35 (1982), 209-271. | MR 644024 | Zbl 0459.60069
- ,[BH86] Potential Theory - An Analytic and Probabilistic Approach to Balayage", Universitext. Springer, Berlin-Heidelberg-New York- Tokyo, 1986. | MR 850715 | Zbl 0706.31001
- , "[BH91]] "Dirichlet Forms and Analysis on Wiener Space", vol. 14 of Studies in Mathematics. de Gruyter, Berlin - New York, 1991. | MR 1133391 | Zbl 0748.60046
- ,[BHH85] Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces, BiBoS (Research Center Bielefeld-Bochum-Stochastics, Bielefeld University). Preprint 54 (1985), 1-70. | MR 887788 | Zbl 0566.31005
- - ,[BHH87] Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces, Exposition. Math. 5 (1987), 97-135. | MR 887788 | Zbl 0659.35025
- - ,[BM68] "Espaces harmoniques associés aux opérateurs différentiels linéaires du second ordre de type elliptique" , Lecture Notes in Mathematics 68, Springer, Berlin - New York, 1968. | MR 241681 | Zbl 0167.40301
- ,[Bon69] Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier (Grenoble) 19 (1969), 277-304. | Numdam | MR 262881 | Zbl 0176.09703
,[Bon70] Opérateurs elliptiques dégénérés associés aux axiomatiques de la théorie du potentiel, In: "Potential Theory" (CIME, 1° Ciclo, Stresa 1969) Edizioni Cremonese, Roma 1970, pp. 69-119. | MR 277744 | Zbl 0205.10704
,[Bou79] Das Picard-Prinzip und verwandte Fragen bei Störung von harmonischen Räumen, Math. Ann. 239 (1979), 247-270. | MR 522783 | Zbl 0377.31011
,[CC72] "Potential Theory on Harmonic Spaces", Grundlehren d. math. Wiss. Springer, Berlin - Heidelberg - New York, 1972. | MR 419799 | Zbl 0248.31011
- ,[CFG86] Harnack's inequality for Schrödinger operators and the continuity of solutions, Proc. Amer. Math. Soc. 98 (1986),415-425. | MR 857933 | Zbl 0626.35022
- - ,[CFZ88] Conditional gauge and potential theory for the Schrödinger operator, Trans. Amer. Math. Soc. 307 (1988), 171-194. | MR 936811 | Zbl 0652.60076
- - ,[CGL93] Harnack's inequality for sum of squares of vector fields plus a potential, Amer. J. Math. 115 (1993), 699-734. | MR 1221840 | Zbl 0795.35018
- - ,[DL54] Les espaces du type Beppo-Levi, Ann. Inst. Fourier (Grenoble) 5 (1953/54), 305-370. | Numdam | MR 74787 | Zbl 0065.09903
- ,[dLP90] Sur les perturbations d'espaces harmoniques, Acad. Roy. Belg. Bull. Cl. Sci. (6) 1 (1990), 201-212. | MR 1146274 | Zbl 0770.31010
,[dLP99] "Sur les perturbations d'espaces harmoniques" Erratum, Acad. Roy. Belg. Bull. Cl. Sci. (6) (1999).
,[FdLP88] Étude de l'équation 1/2Δu - uμ = 0 où μ est une mesure positive, Ann. Inst. Fourier (Grenoble) 38 (1988), 199-218. | Numdam | Zbl 0645.35018
- ,[FOT94] Dirichlet Forms and Symmetric Markov Processes", Studies in Mathematics. de Gruyter, Berlin - New York, 1994. | MR 1303354 | Zbl 0838.31001
- - , "[FS82] Hardy Spaces on Homogeneous Groups", Mathematical Notes 28. Princeton University Press, Princeton, New Jersey, 1982. | MR 657581 | Zbl 0508.42025
- , "[Han81 ] Semi-polar sets and quasi-balayage, Math. Ann. 257 (1981), 495-517. | MR 1513285 | Zbl 0458.31008
,[Han93] A note on continuous solutions of the Schrödinger equation, Proc. Amer. Math. Soc. (2) 117 (1993), 381-384. | MR 1107921 | Zbl 0770.31008
,[Han99] Potentials with given oscillations, Exposition. Math. (1999), to appear. | MR 1706216 | Zbl 0937.31007
,[Her62] Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier (Grenoble) 12 (1962). 415-517. | Numdam | MR 139756 | Zbl 0101.08103
,[Her68] Les fonctions surharmoniques associées à un opérateur elliptique du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 19 (1968), 305-359. | Numdam | MR 261027 | Zbl 0176.09801
- ,[Her72] Les fonctions surharmoniques dans l'axiomatique de M. Brelot associées à un opérateur elliptique dégénéré, Ann. Inst. Fourier (Grenoble) 22 (1972), 131-145. | Numdam | MR 377092 | Zbl 0224.31014
- ,[Her85] Perturbation d' un espace harmonique de M. Brelot. Recherche d' une bijection entre potentiels et potentiels perturbés, Publication de l'Université de Paris 75 (1985). | Zbl 0608.31006
,[Her87] Inégalité de Harnack pour un faisceau perturbé et théorie adjointe, Publication de l'Université de Paris VI 81 (1987).
,[HH87] The Dirichlet problem for sublaplacians on nilpotent Lie groups - geometric criteria for regularity, Math. Ann. 276 (1987), 537-547. | MR 879533 | Zbl 0601.31007
- ,[HK90] Subsolution estimates and Harnack's inequality for Schrödinger operators, J. Reine Angew. Math. 404 (1990), 118-134. | MR 1037432 | Zbl 0779.35026
- ,[HM90] Perturbations by differences of unbounded potentials, Math. Ann. 287 (1990), 553-569. | MR 1066814 | Zbl 0685.31005
- ,[HS82] Uniform bounds for Green functions on C1,1-domains, Ann. Inst. Fourier (Grenoble) 32 (1982), 105-117. | Numdam | MR 658944 | Zbl 0465.35028
- ,[HS84] Quotients of Green functions on R n, Math. Ann. 269 (1984), 263-278. | MR 759112 | Zbl 0535.31004
- ,[Hue88] The domination principle for the sum of squares of vector fields, Exposition. Math. 6 (1988), 183-184. | MR 938182 | Zbl 0655.31008
,[Keu90] Störung harmonischer Räume mit Differenzen beschränkter Potentiale", PhD thesis, Universität Bielefeld, 1990. | Zbl 0744.31006
, "[Kro88] Harmonic spaces associated with parabolic and elliptic differential operators, Math. Ann. 285 (1988), 393-403. | MR 1019709 | Zbl 0664.31011
,[KS93] Hölder continuity of normalized solutions of the Schrödinger equation, Math. Ann. 297 (1993), 663-670. | MR 1245411 | Zbl 0822.35033
- ,[Kur94] Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order, Indiana Univ. Math. J. 43 (1994), 411-440. | MR 1291523 | Zbl 0805.35017
,[Kuw96] On Harnack's inequality for some degenerate elliptic equations, Bull. Fukuoka Univ. Ed. III 45 (1996), 1-7. | MR 1435785 | Zbl 0887.35010
,[LM97] Harnack inequalities for nonsymmetric operators of Hörmander type with discontinuous coefficients, Adv. Math. Sci. Appl. 7 (1997), 833-857. | MR 1476279 | Zbl 0890.35003
- ,[Moh98] Harnack's principle for some non-divergence structure elliptic operators, Comm. Partial Differential Equations 23 (1998), 287-306. | MR 1608528 | Zbl 0897.35022
,[Nak96] Brelot spaces of Schrödinger equations, J. Math. Soc. Japan 48 (1996), 275-298. | MR 1376082 | Zbl 0864.31007
,[Net75] Continuity and maximum principle for potentials of signed measures, Czechoslovak Math. J. 25 (1975), 309-316. | MR 382690 | Zbl 0309.31019
,[NSW85] Balls and metrics defined by vector fields I: Basic properties, Acta Math. 155 (1985), 103-147. | MR 793239 | Zbl 0578.32044
- - ,[SC84] Fundamental solutions and geometry of the sum of squares of vector fields, Invent. Math. 78 (1984), 143-160. | MR 762360 | Zbl 0582.58004
,[Sim90] An elementary proof of Harnack's inequality for Schrödinger operators and related topics, Math. Z. 203 (1990), 129-152. | MR 1030712 | Zbl 0697.35017
,[Zah] Inégalité de Harnack et perturbation d'espaces harmoniques de Brelot par des mesures quelconques, Extracta Math., to appear.
,[Zah96] Fonctionelle additive et ellipticité, Extracta Math. 11 (1996), 288-300. | MR 1437453 | Zbl 0888.31006
,