Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, August 20, 2013.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2013             August 2013           September 2013
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6                1  2  3    1  2  3  4  5  6  7
7  8  9 10 11 12 13    4  5  6  7  8  9 10    8  9 10 11 12 13 14
14 15 16 17 18 19 20   11 12 13 14 15 16 17   15 16 17 18 19 20 21
21 22 23 24 25 26 27   18 19 20 21 22 23 24   22 23 24 25 26 27 28
28 29 30 31            25 26 27 28 29 30 31   29 30



Tuesday, August 20, 2013

2:00 pm in Altgeld Hall 347,Tuesday, August 20, 2013

#### Estimates for the Dirichlet heat kernel on inner uniform domains

###### Janna Lierl (U Bonn)

Abstract: I will present two-sided estimates for the Dirichlet heat kernel on domains that satisfy an inner uniformity condition. This a wide class of domains which can have non-smooth or even fractal boundary, for instance the interior of the Koch snowflake. Gyrya and Saloff-Coste proved two-sided bounds for the Dirichlet heat kernel on unbounded inner uniform domains in a Harnack-type Dirichlet space, i.e. a metric measure space equipped with a strictly local regular Dirichlet form which satisfies a parabolic Harnack inequality. Our estimates extend their result to bounded inner uniform domains. They imply the intrinsic ultracontractivity of the associated semigroup. Moreover, we obtain local estimates for the Dirichlet heat kernel associated with certain non-symmetric forms. For instance, the results apply to any divergence form operator with bounded measurable coefficients and a second order part that is uniformly elliptic and symmetric. This is joint work with Laurent Saloff-Coste.