# Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients

@article{Mazya1968ExamplesON, title={Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients}, author={Vladimir Maz'ya}, journal={Functional Analysis and Its Applications}, year={1968}, volume={2}, pages={230-234} }

#### 58 Citations

On the scientific work of V . G . Maz ’ ya : a personalized account

- 2008

Vladimir Gilelevich Maz’ya, one of the most distinguished analysts of our time, has recently celebrated his 70th birthday. This personal landmark is also a great opportunity to reflect upon the depth… Expand

Local boundedness for solutions of a class of nonlinear elliptic systems

- Mathematics
- 2021

In this paper we are concerned with the regularity of solutions to a nonlinear elliptic system of m equations in divergence form, satisfying p growth from below and q growth from above, with p ≤ q;… Expand

Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth

- Mathematics
- 2021

A partial regularity theorem is presented for minimisers of korder functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an… Expand

Regularity for quasilinear vectorial elliptic systems through an iterative scheme with numerical applications

- Mathematics, Computer Science
- ArXiv
- 2021

Numerical applications as well as applications to higher regularity properties are presented for an iterative procedure to solve quasilinear elliptic systems with p-growth. Expand

Interior estimates in Campanato spaces related to quadratic functionals

- Mathematics
- 2020

In this paper we obtain interior estimates in Campanato spaces for the derivatives of the minimizers of quadratic functionals.

On the generalized Um,pf classes of De Giorgi-Ladyzhenskaya-Ural'tseva and pointwise estimates of solutions to high-order elliptic equations via Wolff potentials

- Mathematics
- 2020

Abstract We consider quasilinear elliptic 2m-order ( m ⩾ 2 ) partial differential equations which prototype is ∑ | α | = m ( − 1 ) | α | D α ( | D m u | p − 2 D α u ) = f ( x ) , x ∈ Ω , where Ω is a… Expand

Singularities of Complex-Valued Solutions to Linear Parabolic Equations

- Mathematics
- International Mathematics Research Notices
- 2020

We construct examples of complex-valued singular solutions to linear, uniformly parabolic equations with complex coefficients in dimension $n \geq 2$, which are exactly as irregular as parabolic… Expand

Bounded solutions of fourth-order nonlinear elliptic equations with convection terms

- Mathematics
- 2019

ABSTRACT We study a Dirichlet problem associated to a nonlinear fourth-order equation with a convective lower order term and with coefficients of principal part satisfying a strengthened coercivity… Expand

Continuity of weak solutions to nonlinear fourth-order equations with strengthened ellipticity via Wolff potentials

- Mathematics
- 2019

In the present article nonlinear fourth-order equations in the divergence form with L^1-right-hand sides and the strengthened ellipticity condition on the coefficients are analyzed. Such equations,… Expand

Davies’ method for heat-kernel estimates: An extension to the semi-elliptic setting

- Mathematics
- 2019

We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are… Expand

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Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder

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Dans des notes aux Doklady de 1961 puis dans un travail recent detaille, Visik [3] a donne une methode generale de resolution pour certains problfemes elliptiques non lineaires [Cf. hypotheses du… Expand

Nonlinear elliptic boundary value problems

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It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The… Expand

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