| 11. |
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| 12. |
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| 13. |
- 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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| 14. |
- 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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| 15. |
- 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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| 16. |
- Karlsson, Mattias, et al.
(författare)
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Monte Carlo dosimetry of the eye plaque design used at the St. Erik Eye Hospital for I-125 brachytherapy
- 2014
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Ingår i: Brachytherapy. - : Elsevier. - 1538-4721 .- 1873-1449. ; 13:6, s. 651-656
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: At St. Erik Eye Hospital in Stockholm, Sweden, ocular tumors of apical height above 6 mm are treated with brachytherapy, using iodine-125 seeds attached to a gold alloy plaque while the treatment planning is performed assuming homogeneous water surroundings. The aim of this work was to investigate the dose-modifying effects of the plaque and the seed fixating silicone rubber glue. METHODS AND MATERIALS: The impact of the gold plaque and silicone rubber glue was studied with the Monte Carlo N-particle transport code, version 5. RESULTS: For the 2 cm most proximal to the plaque surface along the plaques central axis, the eyeball received 104.6-93.0% of the dose in all-water conditions. CONCLUSIONS: The 0.3 mm thick layer of silicone rubber glue, used for seed fixation, attenuates photons little enough to allow characteristic X-rays from the gold alloy plaque to reach the eyeball. Close to the plaque, the dose rates were higher with the plaque and glue present, than in homogeneous water conditions. This is in contrast to what has been reported for more commonly used eye plaques, demonstrating the importance of investigating the dosimetry of individual treatment systems.
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| 17. |
- Lewis, John L., et al.
(författare)
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Regularity of flat free boundaries in two-phase problems for the p-Laplace operator
- 2012
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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. ; 29:1, s. 83-108
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we continue the study in Lewis and Nystrom (2010) [19], concerning the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator, by proving regularity of the free boundary assuming that the free boundary is close to a Lipschitz graph.
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| 18. |
- Lindgren, Erik, et al.
(författare)
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On the two-phase membrane problem with coefficients below the Lipschitz threshold
- 2009
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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. ; 26:6, s. 2359-2372
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Tidskriftsartikel (refereegranskat)abstract
- We study the regularity of the two-phase membrane problem, with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the C-1,C-1-regularity of the solution and that the free boundary is, near the so-called branching points, the union of two C-1-graphs. In our case, the same monotonicity formula does not apply in the same way. In the absence of a monotonicity formula, we use a specific scaling argument combined with the classification of certain global solutions to obtain C-1,C-1-estimates. Then we exploit some stability properties with respect to the coefficients to prove that the free boundary is the union of two Reifenberg vanishing sets near so-called branching points.
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| 19. |
- 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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| 20. |
- Pinchover, Yehuda, et al.
(författare)
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A Liouville-type theorem for the p-Laplacian with potential term
- 2008
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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. ; 25:2, s. 357-368
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p-Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the linear case (p = 2), this condition involves comparison of both the functions and of their gradients.
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