We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free-boundary. As an application we give a full positive answer to a conjecture of De Giorgi on the analyticity of local minimizers of the Mumford-Shah functional.

Department of Oral & Maxillofacial Surgery, Sharavathi Dental College and Hospital, Shimoga, Karnataka, India Department of Periodontics, K.M. Shah Dental College and Hospital, Sumandeep Vidyapeeth, Vadodara, Gujarat, India Department of Oral Medicine & Radiology, Sharavathi Dental College and Hospital, Shimoga, Karnataka, India Department of Conservative and Endodontics, K.M Shah Dental Colleg...

A novel hierarchical Mumford-Shah functional model is addressed to simultaneously segment, denoise and reconstruct the data within a given vector-valued image such as a color image, and to handle important image features such as triple points and other multiple junctions, which can be seen as a hierarchical case of the Mumford-Shah minimal partition problem for vector-valued images. At the same...

This study was conducted to evaluate antioxidant enzyme activities in four caprifig varieties under drought stress and subsequent rewatering in order to screen drought tolerance. Leaf relative water content and membrane stability index significantly reduced under drought stress. ‘Shah Anjir’ and ‘Khormaei’ were able to preserve the highest relative water content and membrane stability index lev...