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Uncertainties associated with integral-based solutions to geodetic boundary-value problems
Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among...
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Boundary value problems in Euclidean space for bosonic Laplacians
A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space...
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Boundary Value Problems
In an initial value problem, the solution of a differential equation is sought which, at time t = t 0 Initial conditions satisfied. In practice, one...
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GPINN with Neural Tangent Kernel Technique for Nonlinear Two Point Boundary Value Problems
Neural networks as differential equation solvers are a good choice of numerical technique because of their fast solutions and their nature in...
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Equivariant index bound for min–max free boundary minimal surfaces
Given a three-dimensional Riemannian manifold with boundary and a finite group of orientation-preserving isometries of this manifold, we prove that...
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A class of moving boundary problems with a source term: application of a reciprocal transformation
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time....
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Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary
The three-dimensional numerical manifold method (3D-NMM), which is based on the derivation of Galerkin’s variation, is a powerful calculation tool...
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Free Boundary Constant p-Mean Curvature Surfaces Intersecting the Pansu Sphere
In the paper, we introduce the notion of free boundary constant p-mean curvature (CPMC) surface in a 3-dimensional pseudohermitian manifold N with...
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Discontinuous Map**s and the Limit Load in Boundary Value Problems of Nonlinear Elasticity
AbstractThe paper considers a boundary-value problem of nonlinear elasticity for a map** (deformation) in two weak formulations: in the form of a...
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Regularity of the One-phase Free Boundaries
This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which...
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Isogeometric Methods for Free Boundary Problems
We present in detail three different quasi-Newton isogeometric algorithms for the treatment of free boundary problems. Two algorithms are based on...
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Smooth and Nonsmooth Duality for Free Time Problems
The main result of this paper contains a representation of the minimum cost of a free time control problem in terms of the upper envelope of...
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Dirac method for nonlinear and non-homogenous boundary value problems of plates
The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on...
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Analytical Solutions to the Cylindrically Symmetric Compressible Navier–Stokes Equations with Density-Dependent Viscosity and Vacuum Free Boundary
In this paper, we investigate the analytical solutions to the cylindrically symmetric compressible Navier–Stokes equations with density-dependent...
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Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite...
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On the Jump Control Problem for Boundary-Value Problems with State-Dependent Impulses
We show how an appropriate parametrization technique and special successive approximations can help to control unknown jumps in the case of nonlinear...
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Obstacle Problems
In this chapter, we study obstacle problems for nonlocal elliptic operators. In order to do so, we first prove the boundary Harnack inequality for...