| 1. |
- Helsing, Johan, et al.
(author)
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Classification of spectra of the Neumann–Poincaré operator on planar domains with corners by resonance
- 2017
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In: 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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Journal article (peer-reviewed)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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| 2. |
- Karlsson, Johannes, et al.
(author)
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Differences in outcome for cervical cancer patients treated with or without brachytherapy
- 2017
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In: Brachytherapy. - Philadelphia, USA : Elsevier. - 1538-4721 .- 1873-1449. ; 16:1, s. 133-140
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Journal article (peer-reviewed)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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| 3. |
- Shahgholian, Henrik, et al.
(author)
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The obstacle problem with singular coefficients near Dirichlet data
- 2017
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In: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier. - 0294-1449 .- 1873-1430. ; 34:2, s. 293-334
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Journal article (peer-reviewed)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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