scholarly journals Viscosity solutions of the Monge–Ampère equation with the right hand side in Lp

2007 ◽  
pp. 221-233
Author(s):  
Barbara Brandolini ◽  
Cristina Trombetti ◽  
Anna Lisa Amadori
2019 ◽  
Vol 45 (1) ◽  
pp. 83-91
Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen

Abstract We prove that if the modulus of continuity of a plurisubharmonic subsolution satisfies a Dini-type condition then the Dirichlet problem for the complex Monge-Ampère equation has the continuous solution. The modulus of continuity of the solution also given if the right hand side is locally dominated by capacity.


2021 ◽  
Vol 73 (1) ◽  
pp. 138-148
Author(s):  
V. V. Hung ◽  
H. N. Quy

UDC 517.9 Recently, Kolodziej proved that, on a compact Kähler manifold the solutions to the complex Monge – Ampére equation with the right-hand side in are Hölder continuous with the exponent depending on and (see [Math. Ann., <strong>342</strong>, 379-386 (2008)]).Then, by the regularization techniques in[J. Algebraic Geom., <strong>1</strong>, 361-409 (1992)], the authors in [J. Eur. Math. Soc., <strong>16</strong>, 619-647 (2014)] have found the optimal exponent of the solutions.In this paper, we construct a cover of the compact Kähler manifold which only depends on curvature of Then, as an application, base on the arguments in[Math. Ann., <strong>342</strong>, 379-386 (2008)], we show that the solutions are Hölder continuous with the exponent just depending on the function in the right-hand side and upper bound of curvature of  


Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen

AbstractWe prove the existence of a continuous quasi-plurisubharmonic solution to the Monge–Ampère equation on a compact Hermitian manifold for a very general measure on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh–Nguyen–Sibony. As a consequence, we give a characterization of measures admitting Hölder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh–Nguyen.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Juhua Shi ◽  
Feida Jiang

AbstractIn this paper, we study the global $C^{1, 1}$ C 1 , 1 regularity for viscosity solution of the degenerate Monge–Ampère type equation $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) with the Neumann boundary value condition $D_{\nu }u=\varphi (x)$ D ν u = φ ( x ) , where the matrix A is under the regular condition and some structure conditions, and the right-hand term B is nonnegative.


1946 ◽  
Vol 11 (1) ◽  
pp. 2-2

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.


VASA ◽  
2010 ◽  
Vol 39 (4) ◽  
pp. 344-348 ◽  
Author(s):  
Jandus ◽  
Bianda ◽  
Alerci ◽  
Gallino ◽  
Marone

A 55-year-old woman was referred because of diffuse pruritic erythematous lesions and an ischemic process of the third finger of her right hand. She was known to have anaemia secondary to hypermenorrhea. She presented six months before admission with a cutaneous infiltration on the left cubital cavity after a paravenous leakage of intravenous iron substitution. She then reported a progressive pruritic erythematous swelling of her left arm and lower extremities and trunk. Skin biopsy of a lesion on the right leg revealed a fibrillar, small-vessel vasculitis containing many eosinophils.Two months later she reported Raynaud symptoms in both hands, with a persistent violaceous coloration of the skin and cold sensation of her third digit of the right hand. A round 1.5 cm well-delimited swelling on the medial site of the left elbow was noted. The third digit of her right hand was cold and of violet colour. Eosinophilia (19 % of total leucocytes) was present. Doppler-duplex arterial examination of the upper extremities showed an occlusion of the cubital artery down to the palmar arcade on the right arm. Selective angiography of the right subclavian and brachial arteries showed diffuse alteration of the blood flow in the cubital artery and hand, with fine collateral circulation in the carpal region. Neither secondary causes of hypereosinophilia nor a myeloproliferative process was found. Considering the skin biopsy results and having excluded other causes of eosinophilia, we assumed the diagnosis of an eosinophilic vasculitis. Treatment with tacrolimus and high dose steroids was started, the latter tapered within 12 months and then stopped, but a dramatic flare-up of the vasculitis with Raynaud phenomenon occurred. A new immunosupressive approach with steroids and methotrexate was then introduced. This case of aggressive eosinophilic vasculitis is difficult to classify into the usual forms of vasculitis and constitutes a therapeutic challenge given the resistance to current immunosuppressive regimens.


2014 ◽  
Vol 76 (1) ◽  
pp. 14-17
Author(s):  
Yoshiyuki KUWAE ◽  
Kunitaka HARUNA ◽  
Yasushi SUGA

Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos

Chapter 8 focuses on threats to construct validity arising from the left-hand side time series and the right-hand side intervention model. Construct validity is limited to questions of whether an observed effect can be generalized to alternative cause and effect measures. The “talking out” self-injurious behavior time series, shown in Chapter 5, are examples of primary data. Researchers often have no choice but to use secondary data that were collected by third parties for purposes unrelated to any hypothesis test. Even in those less-than-ideal instances, however, an optimal time series can be constructed by limiting the time frame and otherwise paying attention to regime changes. Threats to construct validity that arise from the right-hand side intervention model, such as fuzzy or unclear onset and responses, are controlled by paying close attention to the underlying theory. Even a minimal theory should specify the onset and duration of an impact.


2019 ◽  
Vol 3 (Supplement_1) ◽  
Author(s):  
Velarie Ansu ◽  
Stephanie Dickinson ◽  
Alyce Fly

Abstract Objectives To determine which digit and hand have the highest and lowest skin carotenoid scores, to compare inter-and-intra-hand variability of digits, and to determine if results are consistent with another subject. Methods Two subjects’ first(F1), second(F2), third(F3) and fifth(F5) digits on both hands were measured for skin carotenoids with a Veggie Meter, for 3 times on each of 18 days over a 37-day period. Data were subjected to ANOVA in a factorial treatment design to determine main effects for hand (2 levels), digits (4), and days (18) along with interactions. Differences between digits were determined by Tukey's post hoc test. Results There were significant hand x digit, hand x day, digit x day, and hand x digit x day interactions and significant simple main effects for hand, digit, and day (all P < 0.001). Mean square errors were 143.67 and 195.62 for subject A and B, respectively, which were smaller than mean squares for all main effects and interactions. The mean scores ± SD for F1, F2, F3, and F5 digits for the right vs left hands for subject A were F1:357.13 ± 45.97 vs 363.74 ± 46.94, F2:403.17 ± 44.77 vs. 353.20 ± 44.13, F3:406.76 ± 43.10 vs. 357.11 ± 45.13, and F5:374.95 ± 53.00 vs. 377.90 ± 47.38. For subject B, the mean scores ± SD for digits for the right vs left hands were F1:294.72 ± 61.63 vs 280.71 ± 52.48, F2:285.85 ± 66.92 vs 252.67 ± 67.56, F3:268.56 ± 57.03 vs 283.22 ± 45.87, and F5:288.18 ± 34.46 vs 307.54 ± 40.04. The digits on the right hand of both subjects had higher carotenoid scores than those on the left hands, even though subjects had different dominant hands. Subject A had higher skin carotenoid scores on the F3 and F2 digits for the right hand and F5 on the left hand. Subject B had higher skin carotenoid scores on F5 (right) and F1 (left) digits. Conclusions The variability due to hand, digit, and day were all greater than that of the 3 replicates within the digit-day for both volunteers. This indicates that data were not completely random across the readings when remeasuring the same finger. Different fingers displayed higher carotenoid scores for each volunteer. There is a need to conduct a larger study with more subjects and a range of skin tones to determine whether the reliability of measurements among digits of both hands is similar across the population. Funding Sources Indiana University.


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