题目: Nonlinear Partial Differential Equations
报告人:Prof. John Lewis, 美国肯塔基大学
时间: 2014年10月14,16,21,23,28 下午16:30-18:00
地点： 周二 14 21 28 在1518
周四 16 23 在1316
摘要: In this course I plan to lecture on some topics that have interested me for many years
in nonlinear partial differential equations. These topics reflect my function theory background.
Relevant papers of myself and coauthors that I will be lecturing on given time are
 Picard's Theorem and Rickman's Theorem by way of Harnack's Inequality, Proc. of
Amer. Math. Soc.122 (1994), 199 - 206.
 On Some Almost Everywhere Symmetry Theorems (with Andrew Vogel), in Nonlinear
Di usion Equations and Their Equilibrium States, 3(1992), Birkhauser, 347-374 .
 On Pseudospheres, (with Andrew Vogel), Revista Matematica Iberoamericana 7
(1991), 25 - 54 .
 On Pseudospheres that are Quasispheres, (with Andrew Vogel), Rev. Mat. Iberoam.,
17 (2001), 221-255.
 A Symmetry Theorem Revisited, (with Andrew Vogel), Proc. Amer. Math. Soc.,
130 (2001), no. 2, 443-451.
 Symmetry Theorems and Uniform Recti ability, (with Andrew Vogel), Boundary
Value Problems 2007 (2007), 1-59.
 Uniqueness in a Free Boundary Problem (with Andrew Vogel), Communications in
Partial Di erental Equations, 31 (2006), 1591-1614.
 On the Dimension of p Harmonic Measure, (with Bjorn Bennewitz), Ann. Acad.
Sci. Fenn., 30 (2005), 459-505.
 p Harmonic Measure in Simply Connected Domains (with Kaj Nystrom, Pietro Poggi
Corradini), Ann. Inst. Fourier Grenoble 61, 2 (2011)
 Boundary Behaviour and the Martin Boundary Problem for p Harmonic Functions
in Lipschitz Domains (with Kaj Nystrom), Annals of Mathematics 172 (2010), 1907 -
 Boundary Harnack Inequalities for Operators of p Laplace Type in Reifenberg Flat
Domains, (with Kaj Nystrom and Niklas Lundstrom), Proceedings of Symposia in Pure
Mathematics 79 (2008), 229-266.
 Regularity estimates for nonlinear elliiptic and parabolic problems, Editors: Ugo
Gianazza and John Lewis, Springer Lecture Notes in Mathematics 2045 (2012), 1-247.
 Regularity and Free Boundary Regularity for the p Laplacian in Lipschitz and C1
Domains (with Kaj Nystrom), Ann. Acad. Sci. Fenn., 33 (2008), 1 - 26.
 Regularity of
at free boundaries in two phase problems for the p Laplace operator
(with K. Nystrom), Annals Institut H. Poincare Anal. Non Lineaire 29, 1 (2012), 83 -
 Regularity and free boundary regularity for the p- Laplace operator in Reifenberg
flat and Ahlfors regular domains (with K. Nystrom), to appear American Journal of Mathematics.
 On the logarithm of the minimizing integrand for certain variational problems in
two dimensions (with M. Akman and A. Vogel),Journal of Analysis and Mathematical
Physics 2, 1 (2012), 79-88.
 p Harmonic Measure in Space (with K. Nystrom and A. Vogel), J. Eur. Math. Soc.
15 (2013), no. 6, 2197-2256.
 p Harmonic Measure in Simply Connected Domains, Revisited, to appear Transactions
of the American Mathematical Society.
 Murat Akman, On the dimension of a certain measure in the plane, Ann. Acad.
Sci. Fenn. Math. 39 (2014), no. 1, 187-209.
 Hausdor dimension and sigma niteness of some p harmonic measures in space
when p n: (joint with Murat Akman and Andrew Vogel), submitted.
 Sigma- niteness of a certain measure arising from a positive weak solution to a
divergence type pde in space, in preparation (with Murat Akman and Andrew Vogel)