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Results tagged with ap.analysis-of-pdes
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user 49136
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
vote
Weak solution of elliptic differential equation of divergence type
you could also give a look to the paper G.Di Fazio -L^p estimates for divergence form elliptic equations with discontinuous coefficients. Boll. Un. Mat. Ital. A (7) 10 (1996), no. 2, 409–420 where si …
1
vote
Accepted
$L^p$ estimates for elliptic equation of divergence form
You may also give a look to
G.Di Fazio Lp estimates for divergence form elliptic equations with discontinuous coefficients. Boll. Un. Mat. Ital. A (7) 10 (1996), no. 2, 409–420
where leading coeffi …
0
votes
Elliptic regularity in $L^1$
Give a look vere http://www.sciencedirect.com/science/article/pii/0022247X9290285L where Poisson type equation with f in some particular subclass of L1 is studied.
2
votes
fractional laplacian on $\mathbb{R}.$
You may also give a look to the book authored by Molica Bisci - Radulescu and Servadei about fractional operators entitled Variational methods for nonlocal fractional problems.
6
votes
Applications of the Calderon-Zygmund theory to PDE's
starting with the laplacian is a good idea. I suggest Stein old book about Singular integrals.
Then, constant coefficient operators in principal part is just change of choordinates.
Then you could mov …
1
vote
Optimal $L_p$-estimate for elliptic operator
I think you could give a look to the following paper of mine Estimates for Divergence Form Elliptic Equations with Discontinuous Coefficients. You can get it from research gate.
0
votes
Interior gradient estimate for uniformly elliptic equations
You may also give a look to
G.Di Fazio Lp estimates for divergence form elliptic equations with discontinuous coefficients. Boll. Un. Mat. Ital. A (7) 10 (1996), no. 2, 409–420
where leading coeffic …
5
votes
Proof of Littman-Stampacchia-Weinberger theorem on the fundamental solution for elliptic PDEs
the result is in te classical paper
Regular points for elliptic equations with discontinuous coefficients
by LITTMAN, STAMPACCHIA and WEINBERGER.
Another source more easy to read is in the paper "T …
5
votes
On the fundamental solution for elliptic PDE
In the paper The Green Function for uniformly elliptic equations Manuscripta Mathematica Gruter & Widman proved - among other things - pointwise estimates about the gradient of the Green function unde …
2
votes
Higher integrability for Sobolev functions - part 2
I noticed derivative of volume integral is the surface one. Then $\varphi(r) = \int_{B_r}$ satisfies the differential inequality
$$
r\varphi'(r) \leq \varphi(r)
$$
You could deduce properties from tha …
2
votes
Regularity of solution of $(-\Delta + w)f = 0$
regarding the case $f\in L^n$ I can give you some suggestion.
Since $L^n$ is contained in the Morrey space $L^{1,n-1}$ and you have Laplace operator you can say that
$\nabla f $ belongs to BMO and the …
3
votes
General version of Weyl's lemma
unfortunately Weyl lemma cannot be generalized to any divergence form elliptic operator. The problem is given by the smoothness of the coefficients $a_{ij}$. There is a huge literature on the subject. …