Related papers: Obstacle type problems for minimal surfaces
We study a class of semilinear free boundary problems in which admissible functions $u$ have a topological constraint, or spanning condition, on their 1-level set. This constraint forces $\{u=1\}$, which is the free boundary, to behave like…
In this work we present a general introduction to the Signorini problem (or thin obstacle problem). It is a self-contained survey that aims to cover the main currently known results regarding the thin obstacle problem. We present the theory…
In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free…
In this note, we study an obstacle problem for the elastic flow. We prove the local-in-time existence of weak solutions and discuss their relation to classical solutions when additional regularity is obtained. Related results concerning…
In this article we study solutions to the (interior) thin obstacle problem under low regularity assumptions on the coefficients, the obstacle and the underlying manifold. Combining the linearization method of Andersson \cite{An16} and the…
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle…
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more…
We prove the existence and $C^{1,\alpha}$ regularity of solutions to nonlocal fully nonlinear elliptic double obstacle problems. We also obtain boundary regularity for these problems. The obstacles are assumed to be Lipschitz…
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and…
We study optimization problems for partially hinged rectangular plates, modeling bridge roadways, in the presence of real and artificial obstacles. Real obstacles represent structural constraints to avoid, while artificial ones are…
Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries…
We study the higher regularity of free boundaries in obstacle problems for integro-differential operators. Our main result establishes that, once free boundaries are $C^{1,\alpha}$, then they are $C^\infty$. This completes the study of…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions…
In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both for the solution and the free boundary for the…
We study some regularity issues for solutions of non-autonomous obstacle problems with $(p,q)$-growth. Under suitable assumptions, our analysis covers the main models available in the literature.
In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential operators with possibly singular kernels. More precisely, in…
We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part: near regular points the free boundary is $C^\infty$ in space…
We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and…
An examples of solutions of nonlinear differential equations associated with developable, ruled and minimal surfaces are constructed.
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…