标题： Lipschitz连续性和凸性保持性对于Heisenberg群中半线性演化方程解的影响 显示英文标题

标题： Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group

摘要： 在本文中，我们研究赫尔曼群中半线性抛物方程的粘性解。我们证明了在空间无穷远处具有指数增长的粘性解的唯一性。我们还研究了在适当假设下 Lipschitz 和水平凸性保持性质。反例表明，在一般情况下，这些性质在欧几里得空间中的半线性和完全非线性抛物方程中是众所周知的，但在赫尔曼群中并不成立。 显示英文摘要

摘要： In this paper we study viscosity solutions of semilinear parabolic equations in the Heisenberg group. We show uniqueness of viscosity solutions with exponential growth at space infinity. We also study Lipschitz and horizontal convexity preserving properties under appropriate assumptions. Counterexamples show that in general such properties that are well-known for semilinear and fully nonlinear parabolic equations in the Euclidean spaces do not hold in the Heisenberg group.