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The nonlocal s-fractional minimal surface equation for Σ = ∂E where E is an open set in R N is given by H Σ s (p):= RN χE(x) − χEc(x ) dx = 0 for all p ∈ Σ. |x...
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...
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...
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...
We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere S2, ut = ∆u + |∇u|2u in Ω × (0, T) u = ub on ∂Ω × (0, T) u(·, 0) = u0 in Ω, with u(x, t)...
We concern C2-compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are 4, 5 or 6. By conducting a quantitative analysis...
We concern C2-compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are 4, 5 or 6. By conducting a quantitative analysis...
We consider the energy-critical heat equation in ℝn for n ≥ 6 (Formula presented) which corresponds to the L2-gradient flow of the Sobolev-critical energy (Formula presented) Given any k ≥ 2 we find an...
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...
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...
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...
We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere S2, ut = ∆u + |∇u|2u in Ω × (0, T) u = ub on ∂Ω × (0, T) u(·, 0) = u0 in Ω, with u(x, t)...
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