On exterior differential systems involving differentials of Hölder functions

Standard

On exterior differential systems involving differentials of Hölder functions. / Stepanov, Eugene; Trevisan, Dario.

In: Journal of Differential Equations, Vol. 337, 15.11.2022, p. 91-137.

Research output: Contribution to journal › Article › peer-review

Author

Stepanov, Eugene ; Trevisan, Dario. / On exterior differential systems involving differentials of Hölder functions. In: Journal of Differential Equations. 2022 ; Vol. 337. pp. 91-137.

BibTeX

@article{749dc4967a2249549619a6dab504a0ef,

title = "On exterior differential systems involving differentials of H{\"o}lder functions",

abstract = "We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional “rough” signals, i.e. “differentials” of given H{\"o}lder continuous functions interpreted in a suitable way, similarly to Young Differential Equations in Rough Paths theory. This can be seen as a tool to study solvability of exterior differential systems involving rough differential forms, i.e. the forms involving weak (distributional) derivatives of highly irregular (e.g. H{\"o}lder continuous) functions; the solutions (integral manifolds) being also some very weakly regular geometric structures.",

keywords = "Exterior differential systems, Frobenius theorem, Rough paths, Weak geometric structures, Young differential equations",

author = "Eugene Stepanov and Dario Trevisan",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = nov,

day = "15",

doi = "10.1016/j.jde.2022.07.037",

language = "English",

volume = "337",

pages = "91--137",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On exterior differential systems involving differentials of Hölder functions

AU - Stepanov, Eugene

AU - Trevisan, Dario

PY - 2022/11/15

Y1 - 2022/11/15

N2 - We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional “rough” signals, i.e. “differentials” of given Hölder continuous functions interpreted in a suitable way, similarly to Young Differential Equations in Rough Paths theory. This can be seen as a tool to study solvability of exterior differential systems involving rough differential forms, i.e. the forms involving weak (distributional) derivatives of highly irregular (e.g. Hölder continuous) functions; the solutions (integral manifolds) being also some very weakly regular geometric structures.

AB - We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional “rough” signals, i.e. “differentials” of given Hölder continuous functions interpreted in a suitable way, similarly to Young Differential Equations in Rough Paths theory. This can be seen as a tool to study solvability of exterior differential systems involving rough differential forms, i.e. the forms involving weak (distributional) derivatives of highly irregular (e.g. Hölder continuous) functions; the solutions (integral manifolds) being also some very weakly regular geometric structures.

KW - Exterior differential systems

KW - Frobenius theorem

KW - Rough paths

KW - Weak geometric structures

KW - Young differential equations

UR - http://www.scopus.com/inward/record.url?scp=85135825177&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/6d8987a5-eb78-39d4-8085-c369aaee0684/

U2 - 10.1016/j.jde.2022.07.037

DO - 10.1016/j.jde.2022.07.037

M3 - Article

AN - SCOPUS:85135825177

VL - 337

SP - 91

EP - 137

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -

ID: 100611438