liu.seSearch for publications in DiVA
Change search
Link to record
Permanent link

Direct link
BETA
Publications (7 of 7) Show all publications
Ghosh, A., Kozlov, V., Nazarov, S. A. & Rule, D. (2018). A Two Dimensional Model of the Thin Laminar Wall of a Curvilinear Flexible Pipe.
Open this publication in new window or tab >>A Two Dimensional Model of the Thin Laminar Wall of a Curvilinear Flexible Pipe
2018 (English)Report (Other academic)
Abstract [en]

We present a two dimensional model describing the elastic behaviour of the wall of a curved pipe to model blood vessels in particular. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the vessel which itself is allowed to vary. Our two-dimensional model takes the interaction of the wall with the surrounding material and the fluid flowing inside into account and is obtained via a dimension reduction procedure. The curvature and twist of the vessel axis as well as the anisotropy of the laminate wallpresent the main challenges in applying the dimension reduction procedure so plenty of examples of canonical shapes of vessels and their walls are supplied with explicit systems of dierential equations at the end.

Publisher
p. 20
Series
LiTH-MAT-R, ISSN 0348-2960 ; 6
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-148014 (URN)LiTH-MAT-R--2018/06--SE (ISRN)
Available from: 2018-05-24 Created: 2018-05-24 Last updated: 2018-05-24Bibliographically approved
Dindos, M., Pipher, J. & Rule, D. (2017). Boundary value problems for second order elliptic operators satisfying a Carleson condition. Communications on Pure and Applied Mathematics, 70(7), 1316-1365
Open this publication in new window or tab >>Boundary value problems for second order elliptic operators satisfying a Carleson condition
2017 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 70, no 7, p. 1316-1365Article in journal (Refereed) Published
Abstract [en]

Let be a Lipschitz domain in Rn n ≥ 2, and L = divA∇· be a second order elliptic operator in divergence form. We establish solvability of the Dirichlet regularity problem with boundary data in H1,p(@) and of the Neumann problem with Lp(@) data for the operator L on Lipschitz domains with small Lipschitz con- stant. We allow the coefficients of the operator L to be rough obeying a certain Carleson condition with small norm. These results complete the results of [7] where the Lp(@) Dirichlet problem was considered under the same assumptions and [8] where the regularity and Neumann problems were considered on two dimensional domains.

Keywords
Elliptic equations, Carleson measures, Boundary value problems, Lipschitz domains
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-125452 (URN)10.1002/cpa.21649 (DOI)000401720800003 ()
Note

Funding agencies: Engineering and Physical Sciences Research Council [EP/J017450/1]; National Science Foundation DMS Grant [0901139]; CANPDE

Available from: 2016-02-24 Created: 2016-02-24 Last updated: 2017-06-13
Auscher, P., Rosén, A. & Rule, D. (2015). Boundary value problems for degenerate elliptic equations and systems. Annales Scientifiques de l'Ecole Normale Supérieure, 48(4), 951-1000
Open this publication in new window or tab >>Boundary value problems for degenerate elliptic equations and systems
2015 (English)In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 48, no 4, p. 951-1000Article in journal (Refereed) Published
Place, publisher, year, edition, pages
SOC MATHEMATIQUE FRANCE, 2015
Keywords
Littlewood-Paley estimates, functional calculus, bound- ary value problems, second order elliptic equations and systems, weighted norm inequalities.
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-108467 (URN)000363439300006 ()
Note

Funding agencies: ANR project "Harmonic analysis at its boundaries" [ANR-12-BS01-0013-01]; Swedish Research Council, VR [621-2011-3744]

Available from: 2014-06-27 Created: 2014-06-27 Last updated: 2017-12-05
Rodríguez-López, S., Rule, D. & Staubach, W. (2015). On the boundedness of certain bilinear oscillatory integral operators. Transactions of the American Mathematical Society, 367(10), 6971-6995
Open this publication in new window or tab >>On the boundedness of certain bilinear oscillatory integral operators
2015 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 367, no 10, p. 6971-6995Article in journal (Refereed) Published
Abstract [en]

We prove the global L2 × L2 → L1 boundedness of bilinear oscillatory integral operators with amplitudes satisfying a Hörmander type condition and phases satisfying appropriate growth as well as the strong non-degeneracy conditions. This is an extension of the corresponding result of R. Coifman and Y. Meyer for bilinear pseudo-differential operators, to the case of oscillatory integral operators.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2015
Keywords
oscillatory integral operators, bilinear, T(1) Theorem, commutators
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-94272 (URN)000360988500008 ()
Note

Funding: Crawfoord Foundation;  [MTM2010-14946]

Available from: 2013-06-20 Created: 2013-06-20 Last updated: 2017-12-06
Rodríguez-López, S., Rule, D. & Staubach, W. (2014). A Seeger-Sogge-Stein theorem for bilinear Fourier integral operators. Advances in Mathematics, 264, 1-54
Open this publication in new window or tab >>A Seeger-Sogge-Stein theorem for bilinear Fourier integral operators
2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 264, p. 1-54Article in journal (Refereed) Published
Abstract [en]

We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in

and non-degenerate phase functions, from Lp×Lq→Lr under the assumptions that

 and . This is a bilinear version of the classical theorem  of Seeger–Sogge–Stein concerning the Lp boundedness of linear Fourier integral operators. Moreover, our result goes beyond the aforementioned theorem in that it also includes the case of quasi-Banach target spaces.

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
Bilinear Fourier integral operators, Frequency space localization
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-108466 (URN)10.1016/j.aim.2014.07.009 (DOI)000341615100001 ()2-s2.0-84904650922 (Scopus ID)
Available from: 2014-06-27 Created: 2014-06-27 Last updated: 2017-12-05Bibliographically approved
Michalowski, N., Rule, D. & Staubach, W. (2014). Multilinear pseudodifferential operators beyond Calderón–Zygmund theory. Journal of Mathematical Analysis and Applications, 414(1), 149-165
Open this publication in new window or tab >>Multilinear pseudodifferential operators beyond Calderón–Zygmund theory
2014 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 414, no 1, p. 149-165Article in journal (Refereed) Published
Abstract [en]

We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in Lebesgue spaces. These results generalise earlier work of the present authors concerning linear pseudo-pseudodifferential operators. Secondly, we investigate the boundedness of bilinear pseudodifferential operators with symbols in the Hormander S-p,delta(m) classes. These results are new in the case p less than 1, that is, outwith the scope of multilinear Calderon-Zygmund theory.

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
Multilinear pseudodifferential operators; Hormander class symbols; Mixed norm estimates; Bilinear pseudodifferential operators
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-105892 (URN)10.1016/j.jmaa.2013.12.062 (DOI)000332194700013 ()2-s2.0-84893981279 (Scopus ID)
Available from: 2014-04-14 Created: 2014-04-12 Last updated: 2017-12-05Bibliographically approved
Carbery, A., Maz'ya, V., Mitrea, M. & Rule, D. (2014). The integrability of negative powers of the solution of the Saint Venant problem. Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, XIII(2), 465-531
Open this publication in new window or tab >>The integrability of negative powers of the solution of the Saint Venant problem
2014 (English)In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. XIII, no 2, p. 465-531Article in journal (Refereed) Published
Abstract [en]

We initiate the study of the finiteness condition∫ Ω u(x) −β dx≤C(Ω,β)<+∞ whereΩ⊆R n is an open set and u is the solution of the Saint Venant problem Δu=−1 in Ω , u=0 on ∂Ω . The central issue which we address is that of determining the range of values of the parameter β>0 for which the aforementioned condition holds under various hypotheses on the smoothness of Ω and demands on the nature of the constant C(Ω,β) . Classes of domains for which our analysis applies include bounded piecewise C 1 domains in R n , n≥2 , with conical singularities (in particular polygonal domains in the plane), polyhedra in R 3 , and bounded domains which are locally of classC 2 and which have (finitely many) outwardly pointing cusps. For example, we show that if u N is the solution of the Saint Venant problem in the regular polygon Ω N with N sides circumscribed by the unit disc in the plane, then for each β∈(0,1) the following asymptotic formula holds: % {eqnarray*} \int_{\Omega_N}u_N(x)^{-\beta}\,dx=\frac{4^\beta\pi}{1-\beta} +{\mathcal{O}}(N^{\beta-1})\quad{as}\,\,N\to\infty. {eqnarray*} % One of the original motivations for addressing the aforementioned issues was the study of sublevel set estimates for functions v satisfying v(0)=0 , ∇v(0)=0 and Δv≥c>0 .

Place, publisher, year, edition, pages
Scuola Normale Superiore, 2014
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-108526 (URN)000339985500008 ()2-s2.0-84908458320 (Scopus ID)
Available from: 2014-06-29 Created: 2014-06-29 Last updated: 2017-12-05Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-8976-8299

Search in DiVA

Show all publications