Related papers: Free Boundary Formulations for two Extended Blasiu…
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…
A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical…
We define a non-iterative transformation method for Blasius equation with moving wall or surface gasification. The defined method allows us to deal with classes of problems in boundary layer theory that, depending on a parameter, admit…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.
In classical treatment of Maxwell equations, the initial and boundary conditions are introduced by mathematical consideration rather than strictly using the Maxwell equations. As a result, the initial and boundary conditions are not logic…
We consider the free boundary problem for the incompressible elastodynamics equations. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure…
We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type…
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
In this work, we study the asymptotic behavior of the free boundary of the solution to the exterior Bernoulli problem for the half Laplacian when the Bernoulli's gradient parameter tends to $0^+$ and to $+\infty$. Moreover, we show that,…
We introduce a new approach to the study of the crossing equation for CFTs in the presence of a boundary. We argue that there is a basis for this equation related to the generalized free field solution. The dual basis is a set of linear…
This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be…
We compare two singularly perturbed elliptic systems modeling partially phase segregation. Although the formulations are fundamentally different, we prove that their limiting configurations have identical free boundaries. The result shows…
We classify nontrivial, nonnegative, positively homogeneous solutions of the equation \begin{equation*} \Delta u=\gamma u^{\gamma-1} \end{equation*} in the plane. The problem is motivated by the analysis of the classical Alt-Phillips free…
In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of…
In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.
In this survey we go through some of the recent results about the regularity of vectorial free boundary problems of Bernoulli type and free boundary systems. The aim is to illustrate the general methodologies as well as to outline a…
We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.
We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets $\Omega\subseteq A$, and we search for an optimal $A$ in order to minimize a non-linear energy…
This paper is a discussion of relations between some free-boundary problems and infinite dimensional Lie groups; particularly a version of Nahm's equations for the group of Hamiltonian diffeomorphisms in two dimensions.