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Commutator Estimates for Pseudodifferential Operators with Negative Definite Functions as Symbols.

Niels Jacob (1990)

Forum mathematicum

Compactness of bounded quasientropy solutions to the system of equations of an isothermal gas.

Shelukhin, V. V. (2003)

Sibirskij Matematicheskij Zhurnal

Compactness of conformal metrics with positive gaussian curvature in $ℝ^{2}$

Kuo-Shung Cheng, Chang-Shou Lin (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Complex vector fields and hypoelliptic partial differential operators

Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten (2010)

Annales de l’institut Fourier

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields.Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators.Finally we describe a class of compact homogeneous CR manifolds for which the distribution of $(0, 1)$ vector fields satisfies...

Conditions for the time global existence and nonexistence of a compact support of solutions to the Cauchy problem for quasilinear degenerate parabolic equations.

Tedeev, A.F. (2004)

Sibirskij Matematicheskij Zhurnal

Conformal invariance and time decay for non linear wave equations. II

J. Ginibre, G. Velo (1987)

Annales de l'I.H.P. Physique théorique

Conformal invariance and time decay for non linear wave equations. I

J. Ginibre, G. Velo (1987)

Annales de l'I.H.P. Physique théorique

Conservation laws. I: Viscosity solutions.

Yan, Jin, Cheng, Zhixin, Tao, Ming (2007)

Revista Colombiana de Matemáticas

Continuity Estimates for Solutions to the Prescribed-Curvature Dirichlet Problem.

Nicholas J., Simon, Leon Korevaar (1988)

Mathematische Zeitschrift

Continuity of solutions of uniformly elliptic equations in R2.

Yan Yan Li, Sagun Chanillo (1992)

Manuscripta mathematica

Continuous and $L^{p}$ estimates for the complex Monge-Ampère equation on bounded domains in $ℂ^{n}$ .

Darko, Patrick W. (2002)

International Journal of Mathematics and Mathematical Sciences

Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem

Claudio Marchi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators. We establish such an estimate for the parabolic Cauchy problem in the whole space [0, +∞) × ℝn and, under some periodicity and either ellipticity or controllability assumptions, we deduce a similar estimate for the ergodic constant associated to the operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.

Continuous dependence of solutions to mixed boundary value problems for a parabolic equation.

Djibibe, Moussa Zakari, Tcharie, Kokou, Yurchuk, Nikolay Iossifovich (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Continuous dependence on modeling for some well-posed perturbations of the backward heat equation.

Ames, K.A., Payne, L.E. (1999)

Journal of Inequalities and Applications [electronic only]

Control for Schrödinger operators on 2-tori: rough potentials

Jean Bourgain, Nicolas Burq, Maciej Zworski (2013)

Journal of the European Mathematical Society

For the Schrödinger equation, $(i \partial_{t} + \nabla) u = 0$ on a torus, an arbitrary non-empty open set $Ω$ provides control and observability of the solution: $∥u {|_{t = 0}∥}_{L^{2} (𝕋^{2})} \leq K_{T} {∥u∥}_{L^{2} ([0, T] \times Ω)}$ . We show that the same result remains true for $(i \partial_{t} + \nabla - V) u = 0$ where $V \in L^{2} (𝕋^{2})$ , and $𝕋^{2}$ is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for $V \in C (𝕋^{2})$ and conjectured for $V \in L^{\infty} (𝕋^{2})$ . The higher dimensional generalization remains open for $V \in L^{\infty} (𝕋^{n})$ .