H\"older Regularity For Integro-Differential Equations With Nonlinear Directional Dependence

We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also uniform as the order of operators approaches 2

Regularity results for nonlocal fully nonlinear elliptic equations

Rang M. Regularity results for nonlocal fully nonlinear elliptic equations. Bielefeld: Universitätsbibliothek; 2013.In this thesis we consider nonlocal fully nonlinear elliptic operators derived from a certain class of linear integro-differential operators with kernels having anisotropic lower bounds. We obtain regularity estimates for solutions to corresponding nonlocal fully nonlinear elliptic equations

Integro-Differential equations with nonlinear directional dependence

Schwab R, Rang M, Kaßmann M. Integro-Differential equations with nonlinear directional dependence. Indiana University Mathematics Journal. 2014;63(5):1467-1498

Pharmacological differences between the human and rat vanilloid receptor 1 (VR1)

1. Vanilloid receptors (VR1) were cloned from human and rat dorsal root ganglion libraries and expressed in Xenopus oocytes or Chinese Hamster Ovary (CHO) cells. 2. Both rat and human VR1 formed ligand gated channels that were activated by capsaicin with similar EC(50) values. Capsaicin had a lower potency on both channels, when measured electrophysiologically in oocytes compared to CHO cells (oocytes: rat=1.90±0.20 μM; human=1.90±0.30 μM: CHO cells: rat=0.20±0.06 μM; human=0.19±0.08 μM). 3. In CHO cell lines co-expressing either rat or human VR1 and the calcium sensitive, luminescent protein, aequorin, the EC(50) values for capsaicin-induced responses were similar in both cell lines (rat=0.35±0.06 μM, human=0.53±0.03 μM). 4. The threshold for activation by acidic solutions was lower for human VR1 channels than that for rat VR1 (EC(50) pH 5.49±0.04 and pH 5.78±0.09, respectively). 5. The threshold for heat activation was identical (42°C) for rat and human VR1. 6. PPAHV was an agonist at rat VR1 (EC(50) between 3 and 10 μM) but was virtually inactive at the human VR1 (EC(50)>10 μM). 7. Capsazepine and ruthenium red were both more potent at blocking the capsaicin response of human VR1 than rat VR1. 8. Capsazepine blocked the human but not the rat VR1 response to low pH. Capsazepine was also more effective at inhibiting the noxious heat response of human than of rat VR1