SINGULAR PARABOLIC EQUATIONS WITH INTERIOR DEGENERACY AND NON SMOOTH COEFFICIENTS: THE NEUMANN CASE

GENNI FRAGNELLI; DIMITRI MUGNAI

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SINGULAR PARABOLIC EQUATIONS WITH INTERIOR DEGENERACY AND NON SMOOTH COEFFICIENTS: THE NEUMANN CASE

机译：内部退化和非平滑系数的奇异抛物型方程：Neumann案例

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摘要

We establish Hardy - Poincare and Carleman estimates for nonsmooth degenerate/singular parabolic operators in divergence form with Neumann boundary conditions. The degeneracy and the singularity occur both in the interior of the spatial domain. We apply these inequalities to deduce well-posedness and null controllability for the associated evolution problem.

机译：我们建立耐火性 - 庞德，庞大的庞德和卡莱曼估计，在与Neumann边界条件下发散形式的非现实堕落/奇异抛物操作者的估计。在空间域的内部发生退化和奇点。我们应用这些不等式，向相关的演变问题推断出良好的姿势和零可控性。

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《Discrete and continuous dynamical systems▼hSeries S》 |2020年第5期|1495-1511|共17页
作者
GENNI FRAGNELLI; DIMITRI MUGNAI;
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作者单位

Dipartimento di Matematica Universita di Bari 'Aldo Moro'Via E. Orabona 4 70125 Bari Italy;

Dipartimento di Scienze Ecologiche e Biologiche Universita della Tuscia Largo dell’Universita 01100 Viterbo Italy;

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正文语种 eng
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关键词
Carleman estimates; singular/degenerate equations; non smooth coefficients; Hardy–Poincare inequality; Caccioppoli inequality; observability inequality; null controllability;

机译：嘉莱曼估计;奇异/退化等式;非平滑系数;Hardy-Poincare不平等;caccioppoli不平等;可观察性不等式;null可控性;

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专利

1. Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions [J] . Boutaayamou Idriss, Fragnelli Genni, Maniar Lahcen Journal d'analyse mathematique . 2018,第Pta1期

机译：Carleman估计具有内部退化和Neumann边界条件的抛物线方程
2. Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions [J] . Boutaayamou Idriss, Fragnelli Genni, Maniar Lahcen Journal of inverse and ill-posed problems . 2016,第3期

机译：具有内部退化和诺伊曼边界条件的抛物方程的反问题
3. An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy [J] . Khalid Atifi, Idriss Boutaayamou, Hamed Ould Sidi, Abstract and applied analysis . 2018,第6期

机译：具有内部退化的奇异抛物方程的逆源问题
4. Mathematical Model in the Form of a Loaded Second-Order Parabolic-Hyperbolic Equation with a Singular Coefficient [C] . Vadim N. Lesev, Anna O. Zheldasheva, Oksana I. Bzheumikhova, IEEE International Conference on Quality Management, Transport and Information Security, Information Technologies . 2018

机译：具有奇异系数的二阶抛物线-双曲型方程形式的数学模型
5. On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients [D] . Li, Xu. 2013

机译：VMO系数在域中的完全非线性椭圆形和抛物线方程
6. PARABOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS WITH TIME DEPENDENT COEFFICIENTS [O] . 1957

机译：具有时间相关系数的微分方程的抛物线方程组
7. Carleman estimates for singular parabolic equations with interior degeneracy and non smooth coefficients [O] . Fragnelli, Genni, Mugnai, Dimitri 2017

机译：具有内部退化和非光滑系数的奇异抛物方程的Carleman估计

SINGULAR PARABOLIC EQUATIONS WITH INTERIOR DEGENERACY AND NON SMOOTH COEFFICIENTS: THE NEUMANN CASE

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