Smoothness in the Dini Space of a Single Layer Potential for a Parabolic System in the Plane
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-018-4065-9
Abstract: We prove estimates in the Dini space for the second order spatial derivative of a vector parabolic single layer potential. We obtain estimates for higher order derivatives of solutions to initial-boundary-value problems for one-dimensional parabolic… read more here.
Keywords: single layer; smoothness dini; dini space; layer potential ... See more keywords
Gradient of the single layer potential and quantitative rectifiability for general Radon measures
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2021.109376
Abstract: We identify a set of sufficient local conditions under which a significant portion of a Radon measure $\mu$ on $\mathbb{R}^{n+1}$ with compact support can be covered by an $n$-uniformly rectifiable set at the level of… read more here.
Keywords: quantitative rectifiability; radon; single layer; layer potential ... See more keywords
Equi-stress boundaries in two- and three-dimensional elastostatics: The single-layer potential approach
Sign Up to like & getrecommendations! Published in 2017 at "Mathematics and Mechanics of Solids"
DOI: 10.1177/1081286515615001
Abstract: The well-known developments in elastostatics concerning the equi-stressness criterion of optimality for two-dimensional multi-connected unbounded solids under the bulk-dominating load are generalized toward the transient three-dimensional case with rotational symmetry. This paper advances our previous… read more here.
Keywords: three dimensional; single layer; stress boundaries; equi stress ... See more keywords