| 1. |
- Aleksanyan, Gohar, 1987-
(författare)
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Optimal regularity in the optimal switching problem
- 2016
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier. - 0294-1449 .- 1873-1430. ; 33:6, s. 1455-1471
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Tidskriftsartikel (refereegranskat)abstract
- In this article we study the optimal regularity for solutions to the following weakly coupled system with interconnected obstacles{min(−Δu1+f1,u1−u2+ψ1)=0min(−Δu2+f2,u2−u1+ψ2)=0 arising in the optimal switching problem with two modes. We derive the optimal C1,1-regularity for the minimal solution under the assumption that the zero loop set L:={ψ1+ψ2=0} is the closure of its interior. This result is optimal and we provide a counterexample showing that the C1,1-regularity does not hold without the assumption L=L0‾.
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| 2. |
- Ehrnström, Mats, et al.
(författare)
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On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
- 2019
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Ingår i: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1603-1637
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Tidskriftsartikel (refereegranskat)abstract
- We consider the Whitham equation u t +2uu x +Lu x =0, where L is the nonlocal Fourier multiplier operator given by the symbol m(ξ)=tanhξ/ξ. G. B. Whitham conjectured that for this equation there would be a highest, cusped, travelling-wave solution. We find this wave as a limiting case at the end of the main bifurcation curve of P-periodic solutions, and give several qualitative properties of it, including its optimal C 1/2 -regularity. An essential part of the proof consists in an analysis of the integral kernel corresponding to the symbol m(ξ), and a following study of the highest wave. In particular, we show that the integral kernel corresponding to the symbol m(ξ) is completely monotone, and provide an explicit representation formula for it. Our methods may be generalised.
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| 3. |
- Helsing, Johan, et al.
(författare)
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Classification of spectra of the Neumann–Poincaré operator on planar domains with corners by resonance
- 2017
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Ingår i: Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 34:4, s. 991-1011
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Tidskriftsartikel (refereegranskat)abstract
- We study spectral properties of the Neumann–Poincaré operator on planar domains with corners with particular emphasis on existence of continuous spectrum and pure point spectrum. We show that the rate of resonance at continuous spectrum is different from that at eigenvalues, and then derive a method to distinguish continuous spectrum from eigenvalues. We perform computational experiments using the method to see whether continuous spectrum and pure point spectrum appear on domains with corners. For the computations we use a modification of the Nyström method which makes it possible to construct high-order convergent discretizations of the Neumann–Poincaré operator on domains with corners. The results of experiments show that all three possible spectra, absolutely continuous spectrum, singularly continuous spectrum, and pure point spectrum, may appear depending on domains. We also prove rigorously two properties of spectrum which are suggested by numerical experiments: symmetry of spectrum (including continuous spectrum), and existence of eigenvalues on rectangles of high aspect ratio.
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| 4. |
- Indrei, E., et al.
(författare)
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Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems
- 2016
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier. - 0294-1449 .- 1873-1430. ; 33:5, s. 1259-1277
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Tidskriftsartikel (refereegranskat)abstract
- We consider fully nonlinear obstacle-type problems of the form. F(D2u,x)=f(x)a.e. in B1∩Ω,|D2u|≤Ka.e. in B1\Ω, where Ω is an open set and K>0. In particular, structural conditions on F are presented which ensure that W2,n(B1) solutions achieve the optimal C1,1(B1/2) regularity when f is Hölder continuous. Moreover, if f is positive on B-1, Lipschitz continuous, and u≠0⊂Ω, we obtain interior C1 regularity of the free boundary under a uniform thickness assumption on u=0. Lastly, we extend these results to the parabolic setting.
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| 5. |
- Karlsson, Johannes, et al.
(författare)
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Differences in outcome for cervical cancer patients treated with or without brachytherapy
- 2017
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Ingår i: Brachytherapy. - Philadelphia, USA : Elsevier. - 1538-4721 .- 1873-1449. ; 16:1, s. 133-140
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Tidskriftsartikel (refereegranskat)abstract
- Purpose: To compare the clinical outcome of cervical cancer patients treated with primary radiotherapy with and without the addition of brachytherapy.Methods and Materials: In all, 220 patients with cervical cancer stage I-IV treated between 1993 and 2009 were included. Three or five 6.0 Gy fractions of brachytherapy were given in addition to the external beam radiotherapy to 134 patients, whereas 86 patients received external beam radiotherapy alone (EBRTA). In the EBRTA group, the patients received external boost instead of brachytherapy with a total dose to the tumor of 64-72 Gy.Results: The 5-year overall survival and cancer-specific survival rates of the complete series were 42.5% and 55.5%, respectively. The rates of primary complete remission, 5-year cancer-specific survival, and recurrence were 92.5%, 68.5%, and 31.3% for the brachytherapy group vs. 73.3%, 35.4%, and 37.2% for the EBRTA group. The survival (all types) of the patients receiving brachytherapy was significantly (p < 0.0001) better than for the patients treated with external boost, but the difference was most pronounced in FIGO stage II tumors. Higher FIGO stage, nonsquamous cell carcinoma histology, treatment with EBRTA, and lower total equal 2-Gy (EQD2) external dose were significantly associated with poorer survival, lower rate of remission, and higher recurrence rate in multivariate models.Conclusions: Primary tumor remission rate, recurrence rate, and all types of survival rates were improved in the brachytherapy group. Brachytherapy is important to achieve sufficient doses to the periphery and central part of the tumor and should always be considered in treatment of cervical carcinomas.
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| 6. |
- Persson, Maria, et al.
(författare)
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Experience of using MOSFET detectors for dose verification measurements in an end-to-end Ir-192 brachytherapy quality assurance system
- 2018
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Ingår i: Brachytherapy. - : ELSEVIER SCIENCE INC. - 1538-4721 .- 1873-1449. ; 17:1, s. 227-233
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: Establishment of an end-to-end system for the brachytherapy (BT) dosimetric chain could be valuable in clinical quality assurance. Here, the development of such a system using MOSFET (metal oxide semiconductor field effect transistor) detectors and experience gained during 2 years of use are reported with focus on the performance of the MOSFET detectors. METHODS AND MATERIALS: A bolus phantom was constructed with two implants, mimicking prostate and head amp; neck treatments, using steel needles and plastic catheters to guide the Ir-192 source and house the MOSFET detectors. The phantom was taken through the BT treatment chain from image acquisition to dose evaluation. During the 2-year evaluation-period, delivered doses were verified a total of 56 times using MOSFET detectors which had been calibrated in an external Co-60 beam. An initial experimental investigation on beam quality differences between Ir-192 and Co-60 is reported. RESULTS: The standard deviation in repeated MOSFET measurements was below 3% in the six measurement points with dose levels above 2 Gy. MOSFET measurements overestimated treatment planning system doses by 2-7%. Distance-dependent experimental beam quality correction factors derived in a phantom of similar size as that used for end-to-end tests applied on a time-resolved measurement improved the agreement. CONCLUSIONS: MOSFET detectors provide values stable over time and function well for use as detectors for end-to-end quality assurance purposes in 192Ir BT. Beam quality correction factors should address not only distance from source but also phantom dimensions. (C) 2017 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved.
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| 7. |
- Shahgholian, Henrik, et al.
(författare)
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The obstacle problem with singular coefficients near Dirichlet data
- 2017
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier. - 0294-1449 .- 1873-1430. ; 34:2, s. 293-334
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the behaviour of the free boundary close to its contact points with the fixed boundary B boolean AND {x1 = 0} in the obstacle type problem {div(x(1)(a) del u) = X-{u>0} in B+, u=0 on B boolean AND {x(1) = 0} where a < 1, B+ = B boolean AND {x(1) > 0}, B is the unit ball in R-n and n > 2 is an integer. Let Gamma = B+ boolean AND partial derivative{u > 0} be the free boundary and assume that the origin is a contact point, i.e. 0 epsilon (Gamma) over bar. We prove that the free boundary touches the fixed boundary uniformly tangentially at the origin, near to the origin it is the graph of a C-1 function and there is a uniform modulus of continuity for the derivatives of this function.
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| 8. |
- Strömqvist, Martin, 1982-
(författare)
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Harnack's Inequality for Parabolic Nonlocal Equations
- 2019
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1709-1745
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Tidskriftsartikel (refereegranskat)abstract
- The main result of this paper is a nonlocal version of Harnack's inequality for a class of parabolic nonlocal equations. We additionally establish a weak Harnack inequality as well as local boundedness of solutions. None of the results require the solution to be globally positive.
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| 9. |
- Wahlberg, Karin, et al.
(författare)
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Maternal polymorphisms in glutathione-related genes are associated with maternal mercury concentrations and early child neurodevelopment in a population with a fish-rich diet
- 2018
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Ingår i: Environment International. - : Elsevier BV. - 0160-4120 .- 1873-6750. ; 115, s. 142-149
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Tidskriftsartikel (refereegranskat)abstract
- Introduction: Glutathione (GSH) pathways play a key role the metabolism and elimination of the neurotoxicant methylmercury (MeHg). We hypothesized that maternal genetic variation linked to GSH pathways could influence MeHg concentrations in pregnant mothers and children and thereby also affect early life development. Methods: The GCLM (rs41303970, C/T), GCLC (rs761142, T/G) and GSTP1 (rs1695, A/G) polymorphisms were genotyped in 1449 mothers in a prospective study of the Seychellois population with a diet rich in fish. Genotypes were analyzed in association with maternal hair and blood Hg, fetal blood Hg (cord blood Hg), as well as children's mental (MDI) and motor development (PDI; MDI and PDI assessed by Bayley Scales of Infant Development at 20 months). We also examined whether genotypes modified the association between Hg exposure and developmental outcomes. Results: GCLC rs761142 TT homozygotes showed statistically higher mean maternal hair Hg (4.12 ppm) than G carriers (AG 3.73 and GG 3.52 ppm) (p = 0.037). For the combination of GCLC rs761142 and GCLM rs41303970, double homozygotes TT + CC showed higher hair Hg (4.40 ppm) than G + T carriers (3.44 ppm; p = 0.018). No associations were observed between GSTP1 rs1695 and maternal hair Hg or between any genotypes and maternal blood Hg or cord blood Hg. The maternal GSTP1 rs1695 rare allele (G) was associated with a lower MDI among children (β = −1.48, p = 0.048). We also observed some interactions: increasing Hg in maternal and cord blood was associated with lower PDI among GCLC rs761142 TT carriers; and increasing Hg in hair was associated with lower MDI among GSTP1 rs1695 GG carriers. Conclusions: Maternal genetic variation in genes involved in GSH synthesis is statistically associated with Hg concentrations in maternal hair, but not in maternal or fetal blood. We observed interactions that suggest maternal GSH genetics may modify associations between MeHg exposure and neurodevelopmental outcomes.
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