Gustavo Ponce

most citedThe General Quasilinear Ultrahyperbolic Schrödinger Equation

6 citations · 8 across the 3 of their papers we have counts for

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math.AP2005

Decay at infinity of caloric functions within characteristic hyperplanes

L. Escauriaza, C. E. Kenig, G. Ponce +1

It is shown that a function $u$ satisfying, $∣Δ u + \partial_{t} u ∣ \leq M (∣ u ∣ + ∣\nabla u ∣)$ , $∣ u (x, t) ∣ \leq M e^{M ∣ x ∣^{2}}$ in $R^{n} \times [0, T]$ and $∣ u (x, 0) ∣ \leq C_{k} e^{- k ∣ x ∣^{2}}$ in $R^{n}$ and…

math.AP2005★ 6 cited

The General Quasilinear Ultrahyperbolic Schrödinger Equation

C. E. Kenig, G. Ponce, C. Rolvung +1

In this work we establish a local existence theory for the initial value problem associated to the general quasi-linear ultrahyperbolic Schrödinger equation.

math.AP2005★ 2 cited

Variable coefficient Schrödinger flows for ultrahyperbolic operators

C. E. Kenig, G. Ponce, C. Rolvung +1

In this paper we study the local solvability of nonlinear Schrödinger equations of the form $$\p_t u = i {\cal L}(x) u + \vec b_1(x)\cdot \nabla_x u + \vec b_2(x)\cdot \nabla_x \ba…