Related papers: Vectorial Bernoulli Problems and Free Boundary Sys…
In this paper we give a comprehensive treatment of a two-penalty boundary obstacle problem for a divergence form elliptic operator, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and…
In this paper, we have defined the free boundary formulation for two extended Blasius problems. These problems are of interest in boundary layer theory and are deduced from the governing partial differential equations by using appropriate…
The semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove existence of solutions of the incompressible semi-geostrophic equations in a fully three-dimensional domain with a free…
In this paper non-transversal intersection of the free and fixed boundary is shown to hold in any dimension for obstacle problems generated by fully nonlinear uniformly elliptic operators. Moreover, $C^1$ regularity results of the free…
A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is…
We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries
We establish generic regularity results of free boundaries for solutions of the obstacle problem for the fractional Laplacian $(-\Delta)^s$. We prove that, for almost every obstacle, the free boundary contains only regular points up to…
We study the free boundary in an unstable parabolic problem arising from a model in combustion. We consider the physical situation in which the heat advances and prove that the free boundary is a $C^{1,\alpha/2}$ hypersurface.
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of…
In this paper we prove that the free boundary of some variational inequalities with gradient constraints is as regular as the tangent bundle of the boundary of the domain. To this end, we study a generalized notion of ridge of a domain in…
New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary are treated. A harmonic decomposition is used to separate…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
We show a result of maximal regularity in spaces of H\"older continuous function, concerning linear parabolic systems, with dynamic or Wentzell boundary conditions, with an elliptic diffusion term on the boundary.
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
This is the first of two articles in which we investigate the geometry of free boundary and capillary minimal surfaces in balls $B_R\subset\mathbb{S}^3$. In this article, we extend our previous half-space intersection properties to warped…
Model two-dimensional singular perturbed eigenvalue problem for Laplacian with frequently alternating type of boundary condition is considered. Complete two-parametrical asymptotics for the eigenelements are constructed.
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the…
The parabolic obstacle problem for the fractional Laplacian naturally arises in American option models when the assets prices are driven by pure jump L\'evy processes. In this paper we study the regularity of the free boundary. Our main…