# Past OxPDE Special Seminar

21 May 2014
15:00
Dr Dominic Breit
Abstract

We consider degenerate elliptic systems like the p-Laplacian  system with p>1 and zero boundary data. The r.h.s. is given in  divergence from div F. We prove a pointwise estimate (in terms of the  sharp maximal function) bounding the gradient of the solution via the  function F. This recovers several known results about local regularity  estimates in L^q, BMO and C^a. Our pointwise inequality extends also  to boundary points. So these  regularity estimates hold globally as  well. The global estimates in BMO and C^a are new.

• OxPDE Special Seminar
2 May 2014
17:00
Abstract

Morrey's lower semicontinuity theorem for quasiconvex integrands is a classical result that establishes the existence of minimisers to variational problems by the Direct Method, provided the integrand satisfies "standard" growth conditions (i.e. when the growth and coercivity exponents match). This theorem has more recently been refined to consider convergence in Sobolev Spaces below the growth exponent of the integrand: such results can be used to show existence of solutions to a "Relaxed minimisation problem" when we have "non-standard'" growth conditions.

When the integrand satisfies linear coercivity conditions, it is much more useful to consider the space of functions of Bounded Variation, which has better compactness properties than $W^{1,1}$. We review the key results in the standard growth case, before giving an overview of recent results that we have obtained in the non-standard case. We find that new techniques and ideas are required in this setting, which in fact provide us with some interesting (and perhaps unexpected) corollaries on the general nature of quasiconvex functions.

• OxPDE Special Seminar
12 March 2014
16:00
Rosario Mingione
Abstract
• OxPDE Special Seminar
7 March 2014
17:00
Jean Taylor
Abstract
<p>Recent experimental work has determined the atomic structure of a quasicrystalline Cd-Yb alloy. It highlights the elegant role of polyhedra with icosahedral symmetry. Other work suggests that while chunks of periodic crystals and disordered glass predominate in the solid state, there are many hints of icosahedral clusters. This talk is based on a recent Mathematical Intelligencer article on quasicrystals with Marjorie Senechal.</p> <p><br>The seminar will be followed by a drinks reception and forms part of a longer <a href="http://www.maths.ox.ac.uk/groups/oxpde/events/women-pdes">PDE and CoV related Workshop</a>.</p> <p><br>To register for the seminar and drinks reception go to&nbsp;<a href="http://doodle.com/acw6bbsp9dt5bcwb">http://doodle.com/acw6bbsp9dt5bcwb</a></p>
• OxPDE Special Seminar
29 January 2014
15:00
Abstract

In this talk we will show the existence  of a regular "small" weak solution to the flow of the higher dimensional H-systems with initial-boundary conditions. We also analyze its time asymptotic bahavior and we give a stability result.

• OxPDE Special Seminar