Research Plan
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# Research Papers

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