Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Publication

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Xavier Fernandez-Real Girona
2021
Journal Articles

Abstract

We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. with infinite Hn−1 measure. The only two assumptions under which a nice structure result for degenerate points has been established are when φ is analytic, and when Δφ0. Finally, we construct some new examples of free boundaries with degenerate points.

Official source

https://infoscience.epfl.ch/entities/publication/72bf6a8f-cdae-4430-866b-66513329597c

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Xavier Fernandez-Real Girona
2021
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/72bf6a8f-cdae-4430-866b-66513329597c

About this result

Related concepts (32)

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.

Three-dimensional space

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.

Four-dimensional space

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).

Related publications (31)

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Graph Chatbot

How to escape atypical regions in the symmetric binary perceptron: A journey through connected-solutions states

Stable cones in the thin one-phase problem

Dynamical system approach to navigation around obstacles