ABSTRACT. Let be a domain in R2 which is locally convex at each point of its boundary except possibly one, say (0,0), be continuous on /{(0,0)} with a jump discontinuity at (0,0) and f be the unique variational solution of the minimal surface equation with boundary values. Then the radial limits of f at (0,0) from all directions in exist. If the radial limits all lie between the lower and upper limits of at (0,0), then the radial limits of f are weakly monotonic; if not, they are weakly increasing and then decreasing (or the reverse). Additionally, their behavior near the extreme directions is examined and a conjecture of the author’s is proven
Abstract. In this article, we numerically study the regularity loss of the solu-tions of non-paramet...
We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surf...
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free bounda...
ABSTRACT. Let be a domain in R2 which is locally convex at each point of its boundary except possibl...
Let Ω be a domain in R2 which is locally convex at each point of its boundary except possibly one, s...
Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics,...
This monograph treats parametric minimal surfaces of codimension one in the Euclidean space $R^{n+1}...
Many properties of minimal surfaces are of a global nature, and this is already true for the results...
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a seri...
We recall the notion of nonlocal minimal surfaces and we discuss their qualitative and quantitative ...
We recall the notion of nonlocal minimal surfaces and we discuss their qualitative and quantitative ...
Consider a convex domain B of R3. We prove that there exist complete minimal surfaces which are prop...
Click on the DOI link to access the article (may not be free).Consider a solution f is an element of...
In this paper we study the geometric properties, existence, regularity and related issues for a fami...
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a seri...
Abstract. In this article, we numerically study the regularity loss of the solu-tions of non-paramet...
We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surf...
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free bounda...
ABSTRACT. Let be a domain in R2 which is locally convex at each point of its boundary except possibl...
Let Ω be a domain in R2 which is locally convex at each point of its boundary except possibly one, s...
Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics,...
This monograph treats parametric minimal surfaces of codimension one in the Euclidean space $R^{n+1}...
Many properties of minimal surfaces are of a global nature, and this is already true for the results...
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a seri...
We recall the notion of nonlocal minimal surfaces and we discuss their qualitative and quantitative ...
We recall the notion of nonlocal minimal surfaces and we discuss their qualitative and quantitative ...
Consider a convex domain B of R3. We prove that there exist complete minimal surfaces which are prop...
Click on the DOI link to access the article (may not be free).Consider a solution f is an element of...
In this paper we study the geometric properties, existence, regularity and related issues for a fami...
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a seri...
Abstract. In this article, we numerically study the regularity loss of the solu-tions of non-paramet...
We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surf...
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free bounda...