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Embedded tori with prescribed mean curvature

We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form H(X)=1+A|X| −γ for |X| large, when...

A high sensitivity, low noise and high spatial resolution multi-band infrared reflectography camera for the study of paintings and works on paper
Abstract Background Infrared reflectography (IRR) remains an important method to visualize underdrawing and compositional changes in paintings. Older IRR camera systems are being...
A non-compactness result on the fractional Yamabe problem in large dimensions
Let (Xn+1,g+)bean(n+ 1)dimensional asymptotically hyperbolic manifold with conformal infinity (Mn,[ˆh]). The fractional Yamabe problem addresses to solve Pγ[g+,ˆh(u)=cun+2γn−2γ,u>0 on M where c ∈ R and Pγ[g+,ˆh] is the...
Bubbling solutions for Moser-Trudinger type equations on compact Riemann surfaces

We study an elliptic equation related to the Moser–Trudinger inequality on a compact Riemann surface (S,g), Δ gu+λ(ue u 2 −[Formula presented]∫Sue u 2 dv...

Geometry driven type II higher dimensional blow-up for the critical heat equation

We consider the problem vt=Δv+|v|p−1vin Ω×(0,T),v=0on ∂Ω×(0,T),v>0in Ω×(0,T). In a domain Ω⊂Rd, d≥7 enjoying special symmetries, we find the first example of a solution with type II blow-up...

Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula...

Interface Dynamics in Semilinear Wave Equations

We consider the wave equation ε2(-∂t2+Δ)u+f(u)=0 for 0 < ε≪ 1 , where f is the derivative of a balanced, double-well potential, the model case being f(u) = u- u3. For equations of this form, we construct...

Geometry driven type II higher dimensional blow-up for the critical heat equation

We consider the problem vt=Δv+|v|p−1vin Ω×(0,T),v=0on ∂Ω×(0,T),v>0in Ω×(0,T). In a domain Ω⊂Rd, d≥7 enjoying special symmetries, we find the first example of a solution with type II blow-up...

A non-compactness result on the fractional Yamabe problem in large dimensions
Let (Xn+1,g+)bean(n+ 1)dimensional asymptotically hyperbolic manifold with conformal infinity (Mn,[ˆh]). The fractional Yamabe problem addresses to solve Pγ[g+,ˆh(u)=cun+2γn−2γ,u>0 on M where c ∈ R and Pγ[g+,ˆh] is the...
A semilinear elliptic equation with competing powers and a radial potential

We verify the existence of radial positive solutions for the semilinear equation (Formula presented.) where N ≥ 3, p is close to p* ≔ (N+ 2)/(N − 2), and V is a radial smooth potential. If q is super-critical, namely q >...

Nondegeneracy of nodal solutions to the critical Yamabe problem
Monica Musso, Juncheng Wei
Dec 01, 2015
We prove the existence of a sequence of nondegenerate, in the sense of
Duyckaerts–Kenig–Merle [9], nodal nonradial solutions to the critical Yamabe problem−Q = |Q| 2n−2 Q, Q ∈ D1,2(Rn).
This is the first example in the...
Bubbling solutions for Moser-Trudinger type equations on compact Riemann surfaces

We study an elliptic equation related to the Moser–Trudinger inequality on a compact Riemann surface (S,g), Δ gu+λ(ue u 2 −[Formula presented]∫Sue u 2 dv...

Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula...

Green's function and infinite-time bubbling in the critical nonlinear heat equation

Let Ω be a smooth bounded domain in ℝn, n ≥ 5. We consider the classical semilinear heat equation at the critical Sobolev exponent (Equation Presented) Let G(x, y) be the Dirichlet Green function of - A in Q and H(x, y) its...

Interface Dynamics in Semilinear Wave Equations

We consider the wave equation ε2(-∂t2+Δ)u+f(u)=0 for 0 < ε≪ 1 , where f is the derivative of a balanced, double-well potential, the model case being f(u) = u- u3. For equations of this form, we construct...

Nondegeneracy of nodal solutions to the critical Yamabe problem
Monica Musso, Juncheng Wei
Dec 01, 2015
We prove the existence of a sequence of nondegenerate, in the sense of
Duyckaerts–Kenig–Merle [9], nodal nonradial solutions to the critical Yamabe problem−Q = |Q| 2n−2 Q, Q ∈ D1,2(Rn).
This is the first example in the...
A Go/No-Go Decision-Making Model Based on Risk and Multi-Criteria Techniques for Project Selection
The realization of infrastructures and the deployment of processes can follow project formalism. Generally, a project goes through a design and a realization phase. Between these two phases, there is a crucial milestone...

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