bio  website  math.vt.edu/people/renardym 

location  Blacksburg, VA  
age  59  
visits  member for  4 years, 1 month 
seen  4 hours ago  
stats  profile views  2,930 
1d

answered  Companion to theoretical physics for working mathematicians 
1d

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Calculus of variation
@Figueroa: Since distributions can only be approximated by $C^1$ functions, the minimum on $C^1$ functions does not exist; it is only an infimum. 
2d

answered  Calculus of variation 
Dec 20 
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Existence of solution to weak form of linear equation with boundary integral (parabolic PDE)
Using the fact that u is harmonic, you convert $\int_\Omega \nabla u\nabla v$ to $\int_{\partial\Omega}{\partial u\over\partial n}v.$ You then end up with $z_t=Az$, where $A$ is the DirichlettoNeumann map (well studied in the literature). 
Dec 20 
comment 
Existence of solution to weak form of linear equation with boundary integral (parabolic PDE)
Your equation implies that u is harmonic, and with this restriction the trace map is invertible. 
Dec 9 
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$\lVert u\rVert_{W^{2,p}}$ is bounded above by $\lVert \Delta_p u\rVert_{L^2}$ for $u \in W^{1,p}_0 \cap W^{2,p}$?
Have you looked at the onedimensional case? Doing so should answer your question. 
Dec 9 
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Solution of a second order nonlinear ode
What are you hoping for? A miracle? 
Dec 9 
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How to prove it is uniformly bounded?
Since you impose the condition of zero integral, the problem at $\theta=0$ disappears. It is matter of using standard results in perturbation theory. Kato's book is a good reference. 
Dec 8 
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How to prove it is uniformly bounded?
You mean for $\Omega$ to be bounded? If so, more than this is true. You get bounds not just for $\u\_\infty$, but actually for $\u\_{2,\alpha}$. Look up Schauder estimates in any textbook on elliptic PDEs. 
Dec 7 
answered  Estimates on a heat process with fixed boundary data and zero initial conditions 
Dec 4 
answered  $Ax=b$ in a function space 
Dec 4 
revised 
minimizing an integral over integercoefficient polynomials $\displaystyle \inf_{f \in \mathbb{Z}[x]} \int_a^b f(x)^2 \, dx $
I assume you want f to be nonzero, otherwise there is an easy answer. 
Dec 3 
awarded  ap.analysisofpdes 
Dec 3 
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Wellknown or prolific mathematicians that have never written a soleauthor article?
This question does not quite seem to fit this forum and may be closed. But as far as the impact on tenure is concerned, it is of some relevance who the coauthors are. If there are a fair number of them, you can put a positive spin on it. On the other hand, if it is mostly your colleague's thesis advisor, there may be a problem. 
Dec 3 
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Inverse problem to solve out current in the radiation problem
I presume k is fixed in this? Since f has support on [a,a], its Fourier transform is an entire function. And your formula for F gives the Fourier transform of f on the interval [k,k]. Since an entire function is uniquely determined by its values on an interval, the inverse problem has a unique solution. But of course, analytic continuation is a highly illposed problem. On the other hand, most inverse problems are illposed. There is an extensive literature on inverse problems, and the one given here looks fairly typical. Have you made any effort to research the literature? 
Dec 2 
awarded  Nice Answer 
Dec 2 
answered  If $u_m \rightharpoonup u$, how to show using monotonicity that $f(u_m) \rightharpoonup f(u)$? 
Dec 1 
reviewed  Approve Algebraic dependency over $\mathbb{F}_{2}$ 
Nov 29 
comment 
Analytical solution of diffusion PDE with Robin boundary condition
Have you tried separation of variables? 
Nov 23 
comment 
Eigenvalue problem
Your equation becomes hypergeometric under the substitution $u=\exp(\alpha z)$. 