In this paper similarly to the second-order case, we give an elementary and straightforward proof of global Lp estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existen...In this paper similarly to the second-order case, we give an elementary and straightforward proof of global Lp estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases.展开更多
文摘In this paper similarly to the second-order case, we give an elementary and straightforward proof of global Lp estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases.
基金supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905)Shang hai Leading Academic Discipline Project (Grant No. J50101)+3 种基金Key Disciplines of Shanghai Municipality (GrantNo. S30104)Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700)National Natural Science Foundation of China (Grant No. 60532080)the Key Project of Chinese Ministryof Education (Grant No. 306017)
文摘In this paper we obtain local Lp estimates for the parabolic polyharmonic equations by a straightforward approach.
