On parabolic equations for measures. (English) Zbl 1323.35058
Summary: A new existence result is established for weak parabolic equations for probability measures on \(\mathbb R^d\). A priori estimates for solutions of such equations are obtained.
This is a continuation of the authors’ paper [Proc. Lond. Math. Soc., III. Ser. 88, No. 3, 753–774 (2004; Zbl 1072.35076)] giving a considerably weaker sufficient condition for the existence of solutions.
This is a continuation of the authors’ paper [Proc. Lond. Math. Soc., III. Ser. 88, No. 3, 753–774 (2004; Zbl 1072.35076)] giving a considerably weaker sufficient condition for the existence of solutions.
MSC:
35K15 | Initial value problems for second-order parabolic equations |
35R06 | PDEs with measure |
47D07 | Markov semigroups and applications to diffusion processes |
60J35 | Transition functions, generators and resolvents |
60J60 | Diffusion processes |
Keywords:
new existence resultCitations:
Zbl 1072.35076References:
[1] | Bogachev V. I., C. R. Acad. Sci. Paris, Sér. 1 329 pp 705– (1999) |
[2] | Bogachev V. I., Theory Probab. Appl. 45 pp 417– (2000) |
[3] | DOI: 10.1007/PL00008789 · doi:10.1007/PL00008789 |
[4] | Bogachev V. I., Dokl. Russian Acad. Sci. 376 (2001) |
[5] | DOI: 10.1081/PDE-100107815 · Zbl 0997.35012 · doi:10.1081/PDE-100107815 |
[6] | DOI: 10.1016/S0021-7824(00)01187-9 · Zbl 0996.58023 · doi:10.1016/S0021-7824(00)01187-9 |
[7] | DOI: 10.1070/SM2002v193n07ABEH000665 · Zbl 1055.58009 · doi:10.1070/SM2002v193n07ABEH000665 |
[8] | DOI: 10.1112/S0024611503014540 · Zbl 1072.35076 · doi:10.1112/S0024611503014540 |
[9] | Bogachev V. I., Theory Probab. Appl. 50 pp 652– (2005) |
[10] | DOI: 10.1112/blms/bdm046 · Zbl 1129.35039 · doi:10.1112/blms/bdm046 |
[11] | Bogachev V. I., Theory Probab. Appl. 52 pp 240– (2007) |
[12] | DOI: 10.1515/form.2005.17.3.343 · Zbl 1069.60064 · doi:10.1515/form.2005.17.3.343 |
[13] | Gol’dshtein V. M., Quasiconformal Mappings and Sobolev Spaces (1990) |
[14] | Krylov N. V., Stochastic Partial Differential Equations: Six Perspectives pp 185– (1999) |
[15] | Ladyz’enskaya O. A., Linear and Quasilinear Equations of Parabolic Type (1968) |
[16] | Lieberman G. M., Second Order Parabolic Differential Equations (1996) · Zbl 0884.35001 · doi:10.1142/3302 |
[17] | Stannat W., Annali Scuola Normale Super. di Pisa Cl. Sci. (4) 28 pp 99– (1999) |
[18] | DOI: 10.1007/s00028-004-0147-x · Zbl 1136.31313 · doi:10.1007/s00028-004-0147-x |
[19] | Stroock D. W., Multidimensional Diffusion Processes (1979) |
[20] | Wentzell A. D., A Course in the Theory of Stochastic Processes (1981) · Zbl 0502.60001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.