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We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...

Boundary value problems for the 2nd-order Seiberg-Witten equations.

Doria, Celso Melchiades (2005)

Boundary Value Problems [electronic only]

Boundary value problems for the stationary Schrödinger equation on Riemannian manifolds.

Mazepa, E. A. (2002)

Sibirskij Matematicheskij Zhurnal

Branching of asymptotics for elliptic operators on manifolds with edges

S. Rempel, B. W. Schulze (1987)

Banach Center Publications

Breaking of Symmetries for Forced Equations.

E.N. Dancer (1983)

Mathematische Annalen

Bubbling along boundary geodesics near the second critical exponent

Manuel del Pino, Monica Musso, Frank Pacard (2010)

Journal of the European Mathematical Society

The role of the second critical exponent $p = (n + 1) / (n - 3)$ , the Sobolev critical exponent in one dimension less, is investigated for the classical Lane–Emden–Fowler problem $Δ u + u^{p} = 0$ , $u > 0$ under zero Dirichlet boundary conditions, in a domain $Ω$ in $ℝ^{n}$ with bounded, smooth boundary. Given $Γ$ , a geodesic of the boundary with negative inner normal curvature we find that for $p = (n + 1) / (n - 3 - ε)$ , there exists a solution $u_{ε}$ such that $| \nabla u_{ε} |^{2}$ converges weakly to a Dirac measure on $Γ$ as $ε \to 0^{+}$ , provided that $Γ$ is nondegenerate in the sense of second variations of...

Clifford and harmonic analysis on cylinders and torii.

Rolf Sören Krausshar, John Ryan (2005)

Revista Matemática Iberoamericana

Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 < = k ≤ M. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this...

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A 2D climate energy balance model coupled with a 3D deep ocean model.

A class of nonlinear conservative elliptic equations in cylinders

A new type of solutions for a singularly perturbed elliptic Neumann problem.

A prescribing geodesic curvature problem.

A saddle point theorem for non-smooth functionals and problems at resonance.

Almost classical solutions of Hamilton-Jacobi equations.

An Elementary Proof for a Compact Imbedding Result in Generalized Electromagnetic Theory.

An estimate on the hessian of the heat kernel

An upper estimation for the eigenfrequencies of vibrating Liapunoff bodies (first boundary value problem).

Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups

Boundary value problems and layer potentials on manifolds with cylindrical ends