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Free Boundary Problems in Fluid Dynamics
This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary...
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On nonminimizing solutions of elliptic free boundary problems
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily...
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Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems
We are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on...
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Monotonicity formulas for parabolic free boundary problems on cones
Monotonicity formulas play a central role in the study of free boundary problems. In this note, we develop a Weiss-type monotonicity formula for...
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One-phase free-boundary problems with degeneracy
In this paper, we study local minimizers of a degenerate version of the Alt–Caffarelli functional. Specifically, we consider local minimizers of the...
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Free-Boundary Problems for Wave–Structure Interactions in Shallow-Water: DG-ALE Description and Local Subcell Correction
We introduce a robust numerical strategy for the numerical simulation of several free-boundary problems arising in the study of nonlinear...
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Recent Results on Nonlinear Elliptic Free Boundary Problems
In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.
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Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients
In this paper, we prove up to the boundary gradient estimates for viscosity solutions to inhomogeneous nonlinear Free Boundary Problems (FBP)...
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Some Free Boundary Problems Arising in Rock Mechanics
In the article we deal with some physical processes in rock mechanics, which are described by free-boundary problems. Some of them are well known...
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Free End-Time Problems
This chapter provides necessary conditions of optimality for free end-time dynamic optimization problems, that is problems in which the left and...
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Variational Approach to Hyperbolic Free Boundary Problems
This volume is devoted to the study of hyperbolic free boundary problems possessing variational structure. Such problems can be used to model, among...
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Free-boundary problems for holomorphic curves in the 6-sphere
We remark on two free-boundary problems for holomorphic curves in nearly-Kähler 6-manifolds. First, we observe that a holomorphic curve in a geodesic...
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On the Existence of Solutions of Nonlinear Boundary Value Problems for Nonshallow Timoshenko-Type Shells with Free Edges
AbstractWe study the existence of solutions of a boundary value problem for a system of nonlinear second-order partial differential equations for...
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Free boundary problems of the incompressible Navier–Stokes equations with non-flat initial surface in the critical Besov space
Global well-posedness of the Navier–Stokes equations with a free boundary condition is considered in the scaling critical homogeneous Besov spaces
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Free boundary regularity for a class of one-phase problems with non-homogeneous degeneracy
We consider a one-phase free boundary problem governed by doubly degenerate fully nonlinear elliptic PDEs with non-zero right hand side, which should...
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An Adaptive Element-Free Galerkin Approach for Solving Singularly Perturbed Boundary Layer Problems
AbstractThe paper’s objective is to propose a robust and dynamic mesh-free numerical approach to solve singularly perturbed problems(SPPs). As is...
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Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting
A new reformulation of a free boundary problem for the Stokes equations, which govern a viscous flow with an overdetermined condition on the free...
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GENERALIZED EXPONENTIAL BASIS FOR EFFICIENT SOLVING OF HOMOGENEOUS DIFFUSION FREE BOUNDARY PROBLEMS: RUSSIAN OPTION PRICING
This paper develops a method for solving free boundary problems for time-homogeneous diffusions. We combine the complete exponential system of...
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Free Boundary Problems with Local-nonlocal Diffusions and Different Free Boundaries I: Global Solution
We investigate a class of ecological models with local-nonlocal diffusions and different free boundaries. This is Part I of a two-part series, in...
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Boundary pointwise regularity and applications to the regularity of free boundaries
In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give...