Notes on the regularity of harmonic map systems

Notes on the regularity of harmonic map systems

In this note, we provide an alternative proof of C-regularity of continuous weak solutions to the system of harmonic map or heat flow of harmonic maps by Riesz potential estimates between Morrey spaces.

improved regularity of harmonic map flows with hölder continuous energy ∗

For a smooth harmonic map flow u : M× [0, T ) → N with blow-up as t ↑ T , it has been asked ([6], [5], [7]) whether the weak limit u(T ) : M→ N is continuous. Recently, in [12], we showed that in general it need not be. Meanwhile, the energy function E(u(·)) : [0, T ) → R, being weakly positive, smooth and weakly decreasing, has a continuous extension to [0, T ]. Here we show that if this exten...

Notes on the Regularity of Quasiconformal Homeomorphisms

An analogous theorem holds for quasi-conformal homeomorphisms between subdomains of S, as can easily be seen from the fact that all of the above statements are local in nature. Here a.e. refers to the Lebesgue measure on S. Throughout these notes, all measures will be Borel measures on the appropriate topological space, which will always be some Borel subset of R for some n. ”Almost everywhere”...

Regularity of Harmonic Maps

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...