| 1. |
- Adamowicz, Tomasz, et al.
(författare)
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Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points
- 2014
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier Masson / Institute Henri Poincar�. - 0294-1449 .- 1873-1430. ; 31:6, s. 1131-1153
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Tidskriftsartikel (refereegranskat)abstract
- We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for p(.)-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded p(.)-harmonic functions and give some new characterizations of W-0(1,p(.)) spaces. We also show that p(.)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.
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| 2. |
- 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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| 3. |
- Allen, Mark, et al.
(författare)
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The inhomogeneous boundary Harnack principle for fully nonlinear and p-Laplace equations
- 2023
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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. ; 40:1, s. 133-156
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Tidskriftsartikel (refereegranskat)abstract
- We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and p-Laplace-type equations with a right-hand side, as well as for the Laplace equa-tion on nontangentially accessible domains under extra conditions. The approach is completely new and gives a systematic approach for proving similar results for a variety of equations and geometries.
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| 4. |
- Alvino, Angelo, et al.
(författare)
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Well-posed elliptic Neumann problems involving irregular data and domains
- 2010
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Ingår i: ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE. - : GAUTHIER-VILLARS/EDITIONS ELSEVIER, 23 RUE LINOIS, 75015 PARIS, FRANCE. - 0294-1449 .- 1873-1430. ; 27:4, s. 1017-1054
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Tidskriftsartikel (refereegranskat)abstract
- Non-linear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are established under a suitable balance between the integrability of the datum and the (ir)regularity of the domain. The latter is described in terms of isocapacitary inequalities. Applications to various classes of domains are also presented. (C) 2010 Elsevier Masson SAS. All rights reserved.
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| 5. |
- Benedicks, Michael, et al.
(författare)
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Random perturbations and statistical properties of Henon-like maps
- 2006
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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. ; 23:5, s. 713-752
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Tidskriftsartikel (refereegranskat)abstract
- For a large class of non-uniformly hyperbolic diffeomorphisms, we prove stochastic stability under small random noise: the unique stationary probability measure of the Markov chain converges to the Sinai-Ruelle-Bowen measure of the unperturbed attractor when the noise level tends to zero.
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| 6. |
- Björn, Anders, et al.
(författare)
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BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers
- 2010
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Ingår i: ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE. - : GAUTHIER-VILLARS/EDITIONS ELSEVIER, 23 RUE LINOIS, 75015 PARIS, FRANCE. - 0294-1449 .- 1873-1430. ; 27:6, s. 1489-1505
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we use quasiminimizing properties of radial power-type functions to deduce counterexamples to certain Caccioppoli type inequalities and weak Harnack inequalities for quasisuperharmonic functions both of which are well known to hold for p-superharmonic functions We also obtain new bounds on the local integrability for quasisuperharmonic functions Furthermore we show that the logarithm of a positive quasisuperminimizer has bounded mean oscillation and belongs to a Sobolev type space
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| 7. |
- Bona, J L, et al.
(författare)
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Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
- 2005
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Ingår i: Annales de L'Institut Henri Poincaré. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449. ; 22:6, s. 783-797
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Tidskriftsartikel (refereegranskat)abstract
- The generalized Korteweg-de Vries equation has the property that solutions with initial data that are analytic in a strip in the complex plane continue to be analytic in a strip as time progresses. Established here are algebraic lower bounds on the possible rate of decrease in time of the uniform radius of spatial analyticity for these equations. Previously known results featured exponentially decreasing bounds.
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| 8. |
- Carlsson Tedgren, Åsa, et al.
(författare)
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Comparison of high-dose-rate Ir-192 source strength measurements using equipment with traceability to different standards
- 2014
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Ingår i: Brachytherapy. - : Elsevier. - 1538-4721 .- 1873-1449. ; 13:4, s. 420-423
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE:According to the American Association of Physicists in Medicine Task Group No. 43 (TG-43) formalism used for dose calculation in brachytherapy treatment planning systems, the absolute level of absorbed dose is determined through coupling with the measurable quantity air-kerma strength or the numerically equal reference air-kerma rate (RAKR). Traceability to established standards is important for accurate dosimetry in laying the ground for reliable comparisons of results and safety in adoption of new treatment protocols. The purpose of this work was to compare the source strength for a high-dose rate (HDR) (192)Ir source as measured using equipment traceable to different standard laboratories in Europe and the United States.METHODS AND MATERIALS:Source strength was determined for one HDR (192)Ir source using four independent systems, all with traceability to different primary or interim standards in the United States and Europe.RESULTS:The measured HDR (192)Ir source strengths varied by 0.8% and differed on average from the vendor value by 0.3%. Measurements with the well chambers were 0.5% ± 0.1% higher than the vendor-provided source strength. Measurements with the Farmer chamber were 0.7% lower than the average well chamber results and 0.2% lower than the vendor-provided source strength. All of these results were less than the reported source calibration uncertainties (k=2) of each measurement system.CONCLUSIONS:In view of the uncertainties in ion chamber calibration factors, the maximum difference in source strength found in this study is small and confirms the consistency between calibration standards in use for HDR (192)Ir brachytherapy.
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| 9. |
- Dohlmar, Frida, et al.
(författare)
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Validation of automated post-adjustments of HDR prostate brachytherapy treatment plans by quantitative measures and oncologist observer study
- 2023
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Ingår i: Brachytherapy. - : Elsevier BV. - 1538-4721 .- 1873-1449. ; 22:3, s. 407-415
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Tidskriftsartikel (refereegranskat)abstract
- PURPOSE: The aim was to evaluate a postprocessing optimization algorithm's ability to improve the spatial properties of a clinical treatment plan while preserving the target coverage and the dose to the organs at risk. The goal was to obtain a more homogenous treatment plan, minimizing the need for manual adjustments after inverse treatment planning. MATERIALS AND METHODS: The study included 25 previously treated prostate cancer pa-tients. The treatment plans were evaluated on dose-volume histogram parameters established clin-ical and quantitative measures of the high dose volumes. The volumes of the four largest hot spots were compared and complemented with a human observer study with visual grading by eight oncologists. Statistical analysis was done using ordinal logistic regression. Weighted kappa and Fleiss' kappa were used to evaluate intra-and interobserver reliability. RESULTS: The quantitative analysis showed that there was no change in planning target volume (PTV) coverage and dose to the rectum. There were significant improvements for the adjusted treatment plan in: V150% and V200% for PTV, dose to urethra, conformal index, and dose nonhomogeneity ratio. The three largest hot spots for the adjusted treatment plan were significantly smaller compared to the clinical treatment plan. The observers preferred the adjusted treatment plan in 132 cases and the clinical in 83 cases. The observers preferred the adjusted treatment plan on homogeneity and organs at risk but preferred the clinical plan on PTV coverage. CONCLUSIONS: Quantitative analysis showed that the postadjustment optimization tool could improve the spatial properties of the treatment plans while maintaining the target coverage.
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| 10. |
- 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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