Research Plan
Postscript File
# Research Papers

On very weak solutions of certain elliptic systems
Pdflatex File
On some almost everywhere symmetry theorems
* with Andrew Vogel *
Pdflatex File
The Method of Layer Potentials for the Heat Equation in Time
Varying Domains
* with Margaret Murray *
Postscript File
L^2 Solvability and Representation by Caloric Layer Potentials in Time Varying Domains,
* with Steve Hofmann *
Pdf File
The Dirichlet Problem for Parabolic
Operators with Singular Drift Terms * with Steve Hofmann *
Postscript File
The L^p Regularity Problem for the Heat Equation in
Non-cylindrical Domains
* with Steve Hofmann *
Postscript file
On the L^p Neumann and Regularity Problems for the Heat Equation in
Non-cylindrical Domains
* with Steve Hofmann *
Postscript file
Higher Integrability for Parabolic Systems of p Laplacian Type
* with Juha Kinnunen *
Postscript file
Weak Solutions of Parabolic Systems of p Laplacian Type
* with Juha Kinnunen *
Postscript file
On Pseudospheres that are Quasispheres
* with Andy Vogel *
Postscript file
Square Functions of Calder\'{o}n Type and Applications
* with Steve Hoffman *
Postscript file
On the Singular Set in the Navier-Stokes Equations
* with Hi Jun Choe *
Postscript file
The L^p Neumann problem for the heat equation in
non-cylindrical domains * with Steve Hofmann *
Postscript file
On the analyticity of Kato's square root operators
* with Pascal Auscher, Steve Hofmann, Philippe Tchamitchian *
Postscript file
A symmetry theorem revisited
* with Andrew Vogel
*
Postscript file
Existence of big pieces of graphs for parabolic problems
* with Steve Hofmann and Kaj Nystrom *
Postscript File
Caloric measure in parabolic flat domains
/em> with Steve Hofmann and Kaj Nystrom
Postscript File
On Wolff Snowflakes.
* with Gregory C. Verchota and Andrew L. Vogel *
Postscript File
Spectral properties of parabolic layer potentials and
transmission boundary problems in nonsmooth domains.
* with Steve Hofmann and Marius Mitrea *
Postscript File
Symmetry Problems and Uniform Rectifiability,
* with Andrew L. Vogel *
Postscript File
On weak reverse H\"{o}lder inequalities for nondoubling
harmonic measures
* with Bjorn Bennewitz *
Postscript File
On symmetry and uniform rectifiability arising
from some overdetermined elliptic and parabolic boundary
conditions
Postscript File
On the dimension of p harmonic measure
* with Bjorn Bennewitz *
Postscript File
Uniqueness in a free boundary problem
* with Andrew L. Vogel *
Postscript File
Note on p harmonic measure
Postscript File
On a parabolic symmetry problem
* with Kaj Nystrom *
Postscript File
Boundary behaviour for p harmonic functions in Lipschitz
and starlike Lipschitz ring domains
* with Kaj Nystrom *
Postscript File
New results for $p$ harmonic functions,
* with Kaj Nystrom *
Postscript File
The boundary Harnack inequality for infinity harmonic functions
in the plane,
* with Kaj Nystrom *
Postscript File
Boundary behaviour and the Martin boundary problem for
$p$ harmonic functions in Lipschitz domains,
* with Kaj Nystrom *
Postscript File
Regularity and free boundary regularity for the $p$
Laplacian in Lipschitz and $ C^1 $ Domains,
* with Kaj Nystrom *
Postscript File
Boundary behavior of $p$ harmonic functions in domains
beyond Lipschitz domains
* with Kaj Nystrom *
Postscript File
Boundary Harnack inequalities for operators of $p$ Laplace
type in Reifenberg Flat domains,
* with Kaj Nystrom and Niklas Lundstrom *
Pdflatex File
Regularity of Lipschitz free boundaries in two phase
problems for the $p$ Laplacian * with Kaj Nystrom *
Pdflatex File
Regularity of flat free boundaries in two phase
problems for the $p$ Laplace operator * with Kaj Nystrom *
Pdflatex File
p Harmonic functions in simply connected domains
* with Kaj Nystrom and Pietro Poggi Corradini *
Pdflatex File
Cime lecture notes on p harmonic functions
Pdflatex File
Boundary integral operators and boundary value
problems for Laplace's equation
* with TongKeun Chang *
Pdflatex File
$p$ harmonic measure in space
* with Kaj Nystrom and Andrew Vogel *
Pdflatex File
Regularity and free boundary regularity for the p -
Laplace operator in Reifenberg flat and Ahlfors regular domains
* with Kaj Nystrom *
Pdflatex File
On the logarithm of the minimizing integrand for certain
variational problems in two dimensions
with Murat Akman and Andrew Vogel
appeared in * Analysis and Mathematical Physics* (23)
Springer Link or
Pdflatex File
p harmonic measeure in simply connected domains revisited
Pdflatex File
Gradient bounds for p-harmonic systems with vanishing Neumann data in a convex domain.
* with Agnid Banerjee *
Pdflatex File
Hausdorff dimension and sigma finiteness of p harmonic measures when $ p \geq n $ .
* with Murat Akman and Andrew Vogel *
Pdflatex File
Quasi-linear PDE's and low dimensional sets
* with Kaj Nystrom *
Pdflatex File
Sigma finiteness and Hausdorff dimension of a certain Borel measure associated with a positive weak solution to a quasilinear elliptic pde in space
* with Murat Akman and Andrew Vogel *
Pdflatex File
On p Laplace Polynomial Solutions
* with Andrew Vogel *
Pdflatex File
The Brunn Minkowski inequality and a Minkowski problem for nonlinear capacity,
* with Murat Akman, Jasun Gong, Jay Hineman, Andrew Vogel *
Pdflatex File
The Brunn- Minkowski inequality and a Minkowski problem for
A - harmonic Greens function,
* with Murat Akman, Olli Saari, Andrew Vogel *
Pdflatex File
Note on an Eigenvalue Problem,
* with Murat Akman, Andrew Vogel *
Pdflatex File
Note on an Eigenvalue Problem with applications to a Minkowski type regularity problem in R^n.
* with Murat Akman, Andrew Vogel *
Pdflatex File
On a Theorem of Wolff Revisited
* with Murat Akman, Andrew Vogel *
Pdflatex File
Failure of Fatou type theorems for solutions to pde of p-Laplace type in domains with flat boundaries
* with Murat Akman, Andrew Vogel *
Pdflatex File