Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral **Boundary** **Conditions**

**boundary**value

**conditions**. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear

**boundary**value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

8/10 relevant

Preprints.org

Entrainment flow of emerging jet in a half-space with the no-slip
**boundary** **condition**

5/10 relevant

arXiv

Acto-myosin network geometry defines centrosome position

**boundary**

**conditions**the microtubule network is sensitive to. Expand abstract.

**conditions**to centrosome-microtubule networks. Although frequently observed there, the equilibrium position of the centrosome is not systematically at the cell geometrical center and can be close to cell edge. Centrosome positioning appears to respond accurately to the architecture and anisotropy of the actin network, which constitutes, rather than cell shape, the actual spatial

**boundary**

**conditions**the microtubule network is sensitive to. We found that the contraction of the actin network defines a peripheral margin, in which microtubules appeared bent by compressive forces. The disassembly of the actin network away from the cell edges defines an inner zone where actin bundles were absent and microtubules were more radially organized. The production of dynein-based forces on microtubules places the centrosome at the center of this inner zone. Cell adhesion pattern and contractile forces define the shape and position of the inner zone in which the centrosome-microtubule network is centered.

4/10 relevant

bioRxiv

Topology in shallow-water waves: a violation of bulk-edge correspondence

**boundary**

**conditions**with a rich phase diagram, and explain the origin of this mismatch. Expand abstract.

**boundary**condition, showing an explicit violation of the bulk-edge correspondence. We study a continuous family of

**boundary**

**conditions**with a rich phase diagram, and explain the origin of this mismatch. Our approach relies on scattering theory and Levinson's theorem. The latter does not apply at infinite momentum because of the analytic structure of the scattering amplitude there, ultimately responsible for the violation.

7/10 relevant

arXiv

On Neumann problems for elliptic and parabolic equations on bounded manifolds

**boundary**

**conditions**on compact Riemannian manifolds with smooth

**boundary**. We derive oscillation bounds for admissible solutions with Neumann

**boundary**

**condition**$u_\nu = \phi(x)$ assuming the existence of suitable $\mathcal{C}$-subsolutions. We use a parabolic approach to derive a solution of a $k$-Hessian equation with Neumann

**boundary**

**condition**$u_\nu = \phi(x)$ under suitable assumptions.

7/10 relevant

arXiv

Stability of Multidimensional Thermoelastic Contact Discontinuities

**boundary**

**conditions**. Expand abstract.

**boundary**. We identify a stability

**condition**on the piecewise constant background states and establish the linear stability of thermoelastic contact discontinuities in the sense that the variable coefficient linearized problem satisfies a priori tame estimates in the usual Sobolev spaces under small perturbations. Our tame estimates for the linearized problem do not break down when the strength of thermoelastic contact discontinuities tends to zero. The missing normal derivatives are recovered from the estimates of several quantities relating to physical involutions. In the estimate of tangential derivatives, there is a significant new difficulty, namely the presence of characteristic variables in the

**boundary**

**conditions**. To overcome this difficulty, we explore an intrinsic cancellation effect, which reduces the

**boundary**terms to an instant integral. Then we can absorb the instant integral into the instant tangential energy by means of the interpolation argument and an explicit estimate for the traces on the hyperplane.

4/10 relevant

arXiv

General solutions in Chern-Simons gravity and $T \bar T$-deformations

**boundary**

**conditions**and find the

**boundary**stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of

**boundary**

**conditions**in this formalism, such as, including the mixed

**boundary**

**conditions**corresponding to the $T \bar T$-deformation.

7/10 relevant

arXiv

Inverse square singularities and eigenparameter dependent **boundary**
**conditions** are two sides of the same coin

**boundary**

**conditions**to those with inverse square singularities, and vice versa. Expand abstract.

**boundary**

**conditions**containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter with "a negative number of poles". More precisely, we treat in a unified manner one-dimensional Schr\"{o}dinger operators with either an inverse square singularity or a

**boundary**

**condition**containing a rational Herglotz--Nevanlinna function of the eigenvalue parameter at each endpoint, and define Darboux-type transformations between such operators. These transformations allow one, in particular, to transfer almost any spectral result from

**boundary**value problems with eigenparameter dependent

**boundary**

**conditions**to those with inverse square singularities, and vice versa.

10/10 relevant

arXiv

Beyond brane-Higgs regularisation: clarifying the method and model

**conditions**are implemented via essential

**boundary**

**condition**s to be contrasted with the natural boundary conditions derived from the action variation. Expand abstract.

**conditions**for probability currents at the considered flat interval boundaries. Both contribute to the definition of the field geometrical configuration of the model, even in the free case. The BBT could allow to elaborate an ultra-violet origin of the chiral nature of the Standard Model and of its chirality distribution among quarks/leptons. The current

**conditions**are implemented via essential

**boundary**

**conditions**to be contrasted with the natural

**boundary**

**conditions**derived from the action variation. All these theoretical conclusions are confirmed in particular by the converging exact results of the 4D versus 5D approaches. The analysis is completed by a description of the appropriate energy cut-off procedure. The new calculation methods presented, implying the independence of excited fermion masses and 4D Yukawa couplings on the 'wrong-chirality' Yukawa terms, have impacts on phenomenological results like the relaxing of previously obtained strong bounds on Kaluza-Klein masses induced by flavour changing reactions generated through exchanges of the Higgs field.

7/10 relevant

arXiv

Existence of Schrodinger Evolution with Absorbing **Boundary** **Condition**

**boundary**$\partial \Omega$. The question how to compute the probability distribution of the time at which the detector surface registers the particle boils down to finding a reasonable mathematical definition of an ideal detecting surface; a particularly convincing definition, called the absorbing

**boundary**rule, involves a time evolution for the particle's wave function $\psi$ expressed by a Schrodinger equation in $\Omega$ together with an "absorbing"

**boundary**

**condition**on $\partial \Omega$ first considered by Werner in 1987, viz., $\partial \psi/\partial n=i\kappa\psi$ with $\kappa>0$ and $\partial/\partial n$ the normal derivative. We provide here a discussion of the rigorous mathematical foundation of this rule. First, for the viability of the rule it plays a crucial role that these two equations together uniquely define the time evolution of $\psi$; we point out here how the Hille-Yosida theorem implies that the time evolution is well defined and given by a contraction semigroup. Second, we show that the collapse required for the $N$-particle version of the problem is well defined. Finally, we also prove analogous results for the Dirac equation.

7/10 relevant

arXiv